A book that might be helpful is "Not 'Just Friends.'" It has some good information and steps on how to work through affairs, and also how easily they can happen so you can understand them better and avoid the same mistakes in the future.
Personally I'd try to avoid details about the affair for now. Admit having been weak and stupid, but that is the past and you are now focusing on being a better and stronger person. You are focusing on your career and kids... and you want to build up a good friendship with him. Unfortunately this might be really hard for awhile because he's angry and may say a lot of mean hateful things to you out of pain and a need to get that out. Somehow you'll have to find the strength to deal with some of that, give him a lot of space, try to be supportive. He may come through this either wanting to stay, or he may decide he can't handle it and leave. Either way you'll need to work on youself, building a good healthy self-esteem (which should help you avoid unhealthy relationships in the future).
There is no arriving, ever. It is all a continual becoming.
