I agree with Rose76 that you should be doing what is best for the child first and foremost. It doesn't sound like he'll be paying any child support if he doesn't have an income, but in some places you need to at least file for the support in order to qualify for other programs. Whether they stay married or not, his wife is not going to be paying child support for his other kids.

I would try to figure out why I wanted to be with someone who lied and accused me of a crime to my own parents. He sounds like he has some problems. Sometimes we can't be with the people we are in love with. It hurts, but it can be healthier to let go. Good luck with whatever you decide to do.