I apologize for the delay, I did not see your second response. First of all, I am very sorry to hear about your loss. It's not uncommon for a woman who has had ONE miscarriage to experience depression and other emotional issues, and you have had four. If you did not take his wallet, there's nothing you can do to prove it except be honest. If you've never lied to him, he should have no reason to believe you're lying to him now. I think he may be using that as an excuse to not have to deal with your mood swings and whatever else the two of you are going through. You most likely need to seek therapy...as it seems you may not be able to deal with these losses on your own. It's possible he may be using all of this as an excuse to leave so he doesn't have to deal with his loss, which he may also need to seek therapy. This may just be something that you will not be able to deal with on your own.
If he's not cheated or lied to you before, then it's a good chance he's not doing it now, but it does seem as if its very difficult for the two of you to communicate right now. Therapy can help with this. If he's willing to work it out, thats a good sign Try to talk as much as possible, try making lists of the good aspect of your relationship, and the bad. What you like about each other and what can be improved or worked on. Its not going to be easy, and ultimately its going to be your love, compassion, patience and willingness to sacrifice for each other that is going to get you through.
I welcome your thoughts, let me know if you want to talk more.
ps. look into the laws in your area, about leaving the house that you both own. If you do split, you don't want to be accused of abandoning the home.