I have been reading your situation for awhile and you have gotten some excellent advice. I also don't usually chime in to the women on here as I don't feel my communication is the best when interacting with women on here. With you though I feel compelled to reply. I have though two perspectives to share. One is mine and the other is one I witnessed first.
For my experiences...during the first affair I walked a line similar to the one you are walking...acting like a loving spouse and trying some marital counseling. The counseling was useless as I look back in hindsight because my wife didn't want to be there. As for being the loving spouse thinking that would win her back.....all that really did was enable the situation. Eventually I focused completely on galing, myself, and my kids. Treated her as a friend, but nothing more.
During the second affair I did the same even though it was completely hidden under the guise of friendship, but I always new something was wrong.
During the third affair my wife left as it was the only option left and was something that had to happen. I focused on myself and taking care of the family.....detached completely because what she was doing was not in my families best interest. I could no longer let myself or my kids be second fiddle. It also wasn't until this time that my wife started to realize what she was giving up....until she left she always had me as a security rail to fall back on...and I am worth more than that.
For my friend, she also started doing what you are. While she was thrown out of her house, she still communicated daily with her husband and was there for sexual encounters with her husband when he requested it. After a few months of that she realized that she was just a second fiddle to him. A booty call for when he was down and unhappy for a second. The sex wasn't going to bring him back and using sex to keep the connection with him was only enabling his affair. Eventually she ceased sexual relations and limited communication. That really bothered him....really bothered him as he expected her to sit waiting for him. She gal'ed and got a life of her own. While this happened he moved on to a second affair, which eventually ended. It was after this affair ended that he realized what he had given up because his wife wasn't right there for him. I still worry for her as I don't believe he has reached the end of his journey, but that is her issue to deal with now.
In conclusion, until you severe the ties he will not realize what he has. I am not saying to give up on your marriage....more I am saying set boundaries that are based on reality. Would you sleep with a man who was in a relationship with another woman? The truth is right now you are doing that. He is in a relationship with the OW....and you are in reality now the OW.
Yes...he will find ways to turn everything into your fault. That is pretty much the script for any affair. It is mentally easier to blame everyone else for your actions than accept responsibility for them. It is for this reason, that you need to detach and gal. While you do have your part in the collapse of the marriage, it will be hard to reconcile until he accepts his responsibilities in what has happened.
BE strong, gal, and set some boundaries that lay with your personal values......The road will get easier...I promise you that.