Agree with bubblexmas....
Don't give him the luxury of making a leisurely decision. If he is not sure whether he wants out or not, then he should go right now, today, this hour.
You can put this to him non-aggressively - you are not counter-threatening or anything, you are simply being practical. If he is unsure he wants to stay and wants to think about it, then he really, really should try the actual alternative he has in mind for size, and see how much he likes it, because is he sure he's really thought this through?
He should try living alone, arranging visits to the kids and managing them alone when they see him, explaining to his friends and family what's happening, screwing up Xmas, making the money work, housekeeping for one person and he should see how sexually successful he is. All this he should try. It's a "live test". The affair says to me that he's bored of his sex life with you and feels entitled to a better one. In that case he should see how he gets on trying to arrange it.
So today would be a very good day to start. All those bachelor flats start to get let after Xmas. He can look at some tomorrow, it's Saturday.
It may be he can live with all that and like it more. In that case the sooner you all find this out the better. But if I were you I would not be waiting around to hear his decision and hope it's good news.
And of course he needs to understand that, while he figures out if he wants to stay in the marriage, you of course will be reflecting on the same thing. He's welshed on his vows so yours aren't binding any more.
He should be prepared to find that, after 6 months, he wants to come back but in the meantime you've hooked up with a grown-up, so he's now surplus to your requirements.
I know all that sounds a bit in yer face, so tone of voice is all, but it is simply being fair to you. You will proceed with life as you see fit while he figures out what he wants, and if there is room for him later and you both want him back in, then that's the decision. This half-in half-out bullshit is no life for you.
In the short term it makes it easier for him to detach, but if that's where his head is at, then in your shoes I'd want to know now, not when I'm 40, 50 or 60.