I do want to add one more thing. The fact of the matter is that I do feel there's a good chance that he still loves you. In no way am I excusing anything he's done, nor am I suggesting that he should simply be forgiven for his lies to you in the past. As a man, I can tell you that I have made a lot of mistakes in love, and I have been genuinely sorry for the mistakes I've made. I can not say if his apology to you is merely fear of losing the social status of being married, or some other such meaningless drivel, but the two of you are married with children. If you were merely dating, it would make sense to just leave him, but you've a much closer relationship than that, so it does beg the question how much do you want to make it work? Sure, there will always be trust issues, after this, but they can be overcome if you both work at it.