Thank you for contacting JustAnswer.
I am sorry to hear about the problems you are experiencing in your marriage. It is extremely difficult to discover an affair by your spouse. This is a very difficult discovery to make. Lies typically go hand in hand with affairs. This will definitely makes it difficult to trust him. The question is whether he will work to make changes and show you that he deserves to earn your trust back. If he continues to lie, then he is showing you that he is not worthy of your trust. Keep in mind that actions speak louder than words. When deciding whether to trust him, look at what he is doing and showing you, not just what he is saying.
In order for this to be a healthy relationship, we would expect your husband to do a relatively equal amount of emotional work on this relationship as you (if you balance it out over time). This may be one way to evaluate if someone is committed to a relationship and to changing in order to make the relationship work. You deserve someone who will put the work into the relationship as well, since it takes two people to make it work. Also, I definitely believe in trusting your gut. It is often a very good indicator of red flags that should not be ignored. Feelings of love tend to be very irrational, while the gut is a good barometer of danger, both physical and emotional. I hope this is helpful and I wish you the best.
The fact that he has had an affair suggests that there have been problems in your marriage that have not been addressed. Affairs are generally only a symptom of the problem. They may also be a way to try to avoid feeling uncomfortable feelings and facing the problems in the marriage.
Marital therapy can often be a way to discover whether the marriage is able to be fixed or not. I have seen couples who have been able to work through this and make their marriage stronger than before the affair, and I have also seen marriages end due to the affair. Which direction you go in will be up to the two of you and how you are able to work through this. In the meantime, be sure to take care of yourself through healthy eating, exercise, rest and reaching out to supportive people in your life. I hope this answer is helpful. Please let me know if I can clarify further.