There is such a thing as an affair of the heart.
If this woman poses a threat to you in your perception and he is really serious about repairing the marriage, I would think it is important to him that you don't feel threatened. Is this friendship he has more important than his marriage? If he is unwilling to give it up, it says a lot about how he feels for her as well as you.
This is just an opinion, but I hope it helps. Good luck.
I am speaking from a very long difficult experience.