My husband was going to leave at the time of BD but didn't have anywhere else to go. He hasn't really said much about it since really, just once in awhile when he reminds me how bad our marriage was (definitely not true, BTW, I was there too). I suspect there has been/is/whatever an OW (almost 100% sure of at least a long distance EA at the time of BD). I don't know where exactly he is in the process. He is starting to show signs of life again though and there are some positive changes in him - not toward me yet really but some with the kids, the house, the dog, etc. Time will tell. I know he could leave at any time and will believe that until he expresses otherwise. I cope by praying a LOT.
I personally have not felt that I should ask him to leave for various reasons (and I know not everyone here would agree with me). I learned to detach and just focus on me and the kids. It is difficult, but I know right now he can't and won't be my husband or be an active parent and when I am able to stay in that mindset it helps. Seeing glimpses of the "old" him now is making it harder to stay detached but I am working on it.