My H. has been in a R. with o.w. for over 6 mo. now. He has used the term "addiction" to me when talking to me about her. He was away for 6 weeks on a work related issue; came back, and still felt pulled towards her. He had thought the time away would help him get over it.
In the past few days, we have talked a lot and something has happened in his R. with o.w. that has him telling me he only trusts me, that he doesn't believe she really loves him. (See my thread to read up if you are curious). What I'm saying is that by DB'ing and just trying to be his friend through all of this, he has begun to see that I'm the real thing and she is not. Time might help your situation if you can deal with it. It will be hard but if you feel your marriage is something you want to try to save, then give it a chance.
I know it has helped my situation to validate my H.'s "feeings" for o.w. I do not believe that what he feels for her is true love, but he thinks it is right now, so I have been his friend and listened to him, and not put down his feelings (because to him they are important).
I know you're being put into an impossibly difficult situation. A lot of women would not tolerate this. If you choose not to, that is your decision and certainly would be understandable. If you think it is something that may run its course (your H. and o.w.), then it might be worth sticking around for a while, to see how it goes. Let him know you are there for him as a friend; this became very important in my own situation.
Keep taking care of yourself and try to eat and sleep well. I know how hard this is. -Hope
Most of us really marry only once. First love endures, even unto our dying day. And we never really divorce.