I had been talking to a guy 2 years ago who does relationships like this. That he and his wife have found that everything works better for them if she's involved, especially in anything physical. It was weird to me, I had another friend who was interested in being more and so I declined the offer to be in a relationship with the man whose wife would be involved in our relationship.
I'm not interested in dating women, since I'm not sexually interested in them. I'm happy to be friends with women, especially the partners of people that I'm involved with but to have to agree to allow a partner to be an integral part of my relationship is just odd to me. I don't blame you for finding it weird.