he stepped out. I need help

I posted this last night. with some prying, my husband admitted he had a secret account to pay for some premium snapchat. I clicked “forgot password” and reset the password so I could get into the account. and he’s been talking to this girl we went to highschool with (since a little after we had our son three months ago). I can’t see what they’ve talked about because the messages weren’t saved.

he’s swearing that the only thing inappropriate that was said, was she brought up when they hooked up in highschool once and she said “that was fun” and he said “haha yeah it was”

he’s saying the only things they talked about was our problems and they talked about life. not that I believe him at the moment or that it makes it any better if it was mostly innocent. he says he never met up with her

I talked to the girl and she told me the same story. she agreed it was inappropriate because she knew he had a family and she told me she’s really sorry and hopes we can work through it

he’s been crying, i’ve been crying. he said he was scared bc we just got married and had a baby and he panicked and made a mistake. in this timeframe, he’s done a couple other stupid things but not anything like this. he said he will go to counseling with me, will stay away from alcohol and admitted he has a problem getting too drunk, he’s been begging me telling me he’ll do anything to make this better.

what would you do?