I'm so sorry you're going through this, but you're in the right place.
Just because he tells you it's over doesn't make it any better. What does he expect, for you to say "Oh, since it's over that makes it okay, I feel so much better."
This is when the hard work comes in. He broke his vows now he has to prove to you He can be trusted again. To do that he needs to own up to EVERYTHING. There can't be any secrets. He has to give you access to all his accounts, all his passwords, everything. If he says he'll be home by five, he should walk through that door at 4:55.
This is going to be a long roller coaster ride. They say it can take anywhere from 2 to 5 years to fully heal from infidelity.
I'm not sure how he's reacting to all this but there are some wayward spouses who will try to spin it around and blame the betrayed spouse. Don't let this happen. The issues in a relationship are shared 50/50, but he owns the affair 100%.
Remember to take care of yourself during all this. It's going to be hard but try to get plenty of rest and drinking lots of water. I have two small children so I know how difficult it is to take care of yourself, the kids, and deal with this shitstorm our husbands brought down on us.
Sending you lots of (((Hugs)))
Keep posting, it helps.