I need to take this out of the religious framework and talk about it in 21st century terms.
What should you do? Yes, go to counseling. Be 1/2 the relationship. He wants to go to counseling so he can get her to convince you to tell the kids that they have to accept his affair. That's not what you want to go to counseling for. What do you want to go to counseling for? To ask for an equal chance in his heart and mind? That's good. Say that. Stay off his topic. Stay on yours.
Will this save your marriage? Who knows. Will it make you a person who confronts difficult situations and tries to solve them? Yes. Is that a worthwhile thing? Yes.
The chances of saving a marriage doing anything, one way or another when you are confronting an affair of the heart are small. So stand up for who you are and what you want. If this guy can't see the value of a woman who will do this, the next one will. The important thing is that you will respect yourself.