Yep! It has come to this! Now I'm the one saying it:
"Believe none of what he says and half of what he does."
Even if he was staying with you only for the kids (which I doubt very much), that would not preclude him from having an affair.
Look, even if your husband is super-religious, that has yet to stop anyone from having affairs, paying for OWs' abortions, walking out on their family, or snorting coke off strippers. People who want to do those things will not be stopped by obligations, faith, or even plain self-interest in maintaining a career and a public image. They will do it with the same blind compulsion that drives me to go to a hole-in-the-wall diner and eat a sandwich once a month (no matter what diet I'm on--I'm out of control, truly).
Your husband isn't doing any of that. The most simple answer is because he doesn't want to.
And, by the way, staying together for kids means that he gets to spend time with you and the kids and has plenty of opportunity to see how fun and pretty you are. Use that.
Me: 28 H: 30 T: 9 M: 7
WAH: First half of 2017. Round 2 started in Spring 2018.
