I think your sexual desire have to be compatible. It's doesn't sound like they are. If you feel dirty by having sex with him, I think you should find a way to resolve the situation. Maybe that means him getting into therapy or something, or maybe it means finding someone else. Have you talked to him about this? Tell him that it creeps you out?

Is the house really worth staying with him? Can you get out of it, if this relationship is that bad? It sounds like this obsession is beyond the point of repair and is a part of him. I wish I had better advice, but I have never had experience with this. Maybe it was a past trauma or something from childhood.