OP, this is an unbearable time for you, I'm sorry. My DH did something similar a couple of years ago, we met and married young (although only had kids after 5 years of marriage). At the time everyone was telling me there must be another woman, I couldn't believe it as he was always such a devoted husband/dad, plus he is a school teacher so not much opportunity for that. I only found out via his email, flirty emails to Ow during school time and school trips planned as such they would supervise together.
As it turned out, the MLC was the catalyst for the affair, the affair was a symptom of a deeper problem. I threw him out for about a month, it is important to try to retain some control of your life and remember it is kit as much YOUR decision to have him back as it is HIS. I know it's hard, but don't sit around reminiscing, hoping and praying he will come back. You really need to try to continue with life, see friends, do hobbies, get some exercise whatever makes you feel good.
After a couple of weeks I was actually beginning to enjoy doing everything my way without having to consider his needs! I actually made a list of positives is he really didn't want to be with me anymore!
I am not saying it will be easy and there of course will be times you feel low. At the moment you are in shock and like me, will probably be desperate to have him back and just get your life back to normal. But if he really wants out, you may as well let him go as the last thing you want is someone who feels "forced" to be around.
As it turned out my DH and I stayed together but a LOT Of things had to change (on both our parts). I still don't know whether I will ever trust him 100% again, and possibly even stronger is the feeling that he might up and leave us all suddenly, out of the blue like he did that last time. He swears it'll never happen again but I never expected it to happen the first time.
So do you really want to love like that? Could it be you're better off without him? I'm not saying you are, it's just a thought.