Expect to find out more op 
I've been where you are and it's hell. It's good you have RL support, I found this invaluable to my sanity.
I'm still with dp 18 months on. It can work but it isn't easy.
You will be in the shell shocked stage at the moment and expect to go through every emotion at the flick of a switch.
Don't make any decisions about your future at the moment. You will be in a fog like existence and until that lifts you won't see clearly how you see yourself in the future.
Most importantly is the way your dh responds to this. He is possibly minimising, you may find out more in the coming weeks. At the moment he sounds remorseful but be careful as those tears might well be for himself. Remember how selfish he's been, he's been caught out, now he has to suffer the consequences.
Hysterical bonding - read up on this. If you stay together this may well happen. It's temporary.
Have you been recommended the book by Shirley Glass - Just 'Good Friends' - worth getting whether you plan on staying together or not. For your dh to read too.
I don't think a ate or slept for over a week. Your body is possibly running on adrenaline right now. Be kind to yourself. Let your dh look after the dc while you meet your RL friends who can support you and just let you talk it through.
I've guessed at the part time job your dh does. I think this all needs to change now doesn't it and he needs to join the adult world, there's no reason why he can't work in the day now is there? These are some immediate changes I would insist on.
Take care OP. sorry for the mish mash of information.