Asked an answered, M. This conversation needs to take place with your HUSBAND, not the OW.
Have you read the book "NOT Just Friends" yet? It's by Shirley Glass, and it is THE definitive work on emotional affairs, which is what your husband and this woman appear to be having.
The problem with confronting OW/OM (well, one of MANY problems with it) is that most betrayed spouses will assume the OW/OM is dealing honorably, when -- by definition -- they are NOT. They are predators, pure and simple, and this woman is NO friend of your marriage, trust me on this one.
I'd suggest you treat her civilly, and no more. If she asks you if something is upsetting you, I would say "I think we both know what that is," and leave it at that.
