You do have a confusing situation. Usually a separated couple that has two kids together also has a divorce agreement that gives them guidelines for how to do what's best for their kids. And some are very cooperative about managing their kids together--but they're usually pretty clear within a year after their breakup whether they're going to sleep together or not. But because you were never legally married (though you might have come close to the definition of "common law cohabitation" in your part of Canada) you have not been inclined to make your post cohabitational relationship guidelines explicit either.
Do you have a clear agreement about child support? If not the very vagueness of his responsibility towards the children may actually be promoting his reticence to get involved with anyone else, and the frequency with which you see each other may be preventing both of you from letting go of enough of the relationship to even experience the mourning process and begin to get ready to move on towards a new partnership some time in the future.
Since you've known him for 10 years, it would actually be normal for it to take up to 5 years for your breakup to be completed--and your agreement to remain "friends" is definitely retarding your internal processes of separation. You are perfectly normal to be feeling jealousy, because behind the face of "friends" your love feelings can come and go at will, and he's doing nothing to stop them either.
It sounds like he has a good job and gives you enough money for what the kids need, so you are allowing him to determine from month to month what your relationship will be, and you're submitting to the label of "friends," even though you are not comfortable with it. It's even possible that you don't feel safe demanding anything from him, because you fear that he could "downgrade" his definition of "friends" if he doesn't like something--including even any expression of jealousy on your part. And whether you CALL it LOVE or not, it IS love, and hurt and jealousy are virtually inevitable as long as the relationship guidelines allow him to do whatever he wants and you're dependent financially but have not ever asserted any rights. Have you sought legal advice about the children's rights to his financial support, and your own rights as well?
I'll hear from you tomorrow, and specifically what do you want with him? What commitments?
I had to switch to Q & A and even write a short followup for the computer system to allow me to answer more now. But there's something very important I want to add. I have recently concluded, from lots of research in love histories, including my own, and from studies and therapy using Jungian psychology, that our "First Great Love" has as much lifelong effect on us as each of our parents, though less deep-seated because it didn't begin anywhere near as early or when our mental and emotional equipment for reception were as primitive as they were before age 5. You started yours at 16, which is plenty early as they normally can be.
This first great love becomes a "complex" which I believe is concretely an interconnected structure of neurons in our cerebellum, or little brain below and behind the rest of our brain, where we typically also intuitively locate our unconscious minds--below and behind the rest of our minds. This FirstPartnerComplex functions like the complex of physical driver programs collected to enable us to ride a bicycle without any effort to remember how, even 50 to 70 years after the last time we rode a bicycle. Only this complex is not just designed for physical and perceptual performance on a bicycle. It includes thoughts, emotions, perceptions, expectations, and actions in relationship to mother, to father, and later to our First Great Love, or First Marital Partner, IF that partnership has lasted at least 2 years and involved as complete a personal commiment to "we-ness" as we were capable of at the time--even if we held back from marriage at that time. I suspect that holding back from marriage was not as important to you as it was to him.
I can't insist I'm correct, and the research literature in the West has not drawn such a conclusion yet, probably because nobody really wants to do that, since it might threaten our "anything goes" serial monogamy model in present times. In India traditional culture it is expected that one's FIRST LOVE, the first one that the family allows, that is, will be the ONLY truly passionate love of one's entire lifetime. Men before, and now increasingly women also, are allowed to remarry (mainly if their first love dies), but that's expected to be "companionship love" only, and it's unseemly to express as much passion the second time around. Muslims in the Middle East are allowed to divorce within the first year or so of their (arranged) marriages, perhaps because it's assumed that the natural FirstLove bonding cement hasn't fully hardened yet, so it will be possible to completely reset a new love as the FirstPartnerComplex that will then govern one's unconscious mate choices and expectations thereafter. Prophet Mohammed ("peace be upon him") was once asked by a woman who had had 4 husbands, because each one had died, which of her husbands she would find herself spending Eternity with after her death; and he responded "the one you loved the most."
I'm addressing this issue, because I think it's likely that you will never really "get over" the image & expectations you've developed of your first love for the rest of your life, especially not if you continue to keep the door of your heart open to him as he has determined with his decree that you will continue as "friends." I have to hedge this statement, however. IF you come to NOT want him anymore, perhaps because you don't want a relationship LIKE the one you have had with him, or you come to dislike who and what he is, values and aspires to as a person, then you will be able to choose a different person, and/or different kind of partner for a future couple relationship. [I did that, sought and found a Different Kind of Coupling--more equal in power and more inspiration and learning for me FROM her, just 12 years after the breakup of my first love of 9 years, which luckily for me and her had produced no children. But I am still easily aware of what I had before and how good it felt most of the time. I don't want her or that relationship back, consciously. But it's there outside of my conscious mind. That's why SO MANY PEOPLE say "Why do I keep finding the same kind of guys/women to fall in love with?"]
It's mainly through conscious awareness of what your regressive (& first-love-cloning) tendensies are--we all have them--that you can be vigilant enough to avoid trying the same kind of person and relationship over again. So psychotherapy, journaling, dream writing and interpretation, meditation and other approaches are much more necessary if you want to get over your first love as a love-pattern establishment, than if you want to stay married to your first love or just keep marrying the same kind of person for a decade or two before shifting patterns somewhat.
So is would suggest that you talk to your "friend-child-father" about this possibility--even though there is not, to my knowledge an already popularly recognized authority who preaches what I've just written. (There is however, in USA also a tradition of second or third marriages in which one partner has succeeded in getting a differently patterned relationship established, usually by being acutely aware of what she or he DOES NOT want to duplicate--so it's not routinely hopeless to achieve a change.)
It would be interesting to me to know why he's convinced he doesn't want to be "more than friends" with you anymore. For it's possible that's based on a psychological barrier inside of him, and/or you, that could be melted down with sufficient psychological insight and emotional repatterning (Emotionally Focused Couples Therapy, centered in U of Ottawa and online for the emotional part).
I think you two deserve to know now, rather than just 5-10 years from now, that you're not going to "get over" your attachment to each other without a LOT of repeated heartache to drive you apart (for self-protection). And even then you may be more inclined to tolerate half-committed relationships rather than risk the unprecedented duration of low-grade dissatisfaction ("better than nobody though") you could face from here on out.
In my estimation, It would be better to get into couples counseling to either discover the emotional roots of your current distance and actually construct a new and more robust couple love commitment than you've ever had, or to discover how and why your lives could never fit together more closely again and then negotiate an emotional and psychic separation that works for your children and for getting your own lives onto individual development trajectories that you were probably nowhere near ready for when you first became sweethearts. Either of these outcomes would be better for your children too.