It is amazing how I see the exact thing I am going through pop up again and again here on SI. I have even brought this very question up with our therapist.
My H has gone so far as to say he doesn't even recognize himself in the A at this point, and it has only been 3 months since D Day.
I don't have a great answer other than to say that the affair was a crisis in our marriage. My H's coping mechanisms gave out, and he did a selfish, destructive, terrible thing.
I also have problems reconciling the person he is now with the person sneaking around, other than to know that his actions then weren't really about me. They were solely about him. He is working now to be the best husband he can be, and what I am getting now may be an idealized version of him. But, with therapy and a lot of introspection, I think the important parts can stick.
I feel closer than I ever have to him. I have to hope that there will be a strong pull for both of us to keep it this way. Of course, there is a lot of sh*t to work through, and a lot of bad days to come. A lot of hurt. But, we are all complicated people who, in the end, just want to be seen, loved and accepted for who we are. That's my belief. anyway.