Asking for what you want
There's nothing wrong with wanting a relationship that your boyfriend has nothing to do with. He should not assume the people you date will have sex with him. If that is what he thought this relationship style was--a chance for him to have a threesome--then he did not understand this relationship style at all. Your relationship with your girlfriend is not about him--end of story!
Some relationships are like that--three people together--but that is not something someone can assume for someone else. The world does not revolve around penises, and women are not commodities or toys. Your boyfriend should respect your desire to be an independent sexual agent.
Him wanting your girlfriend to be his unicorn does not make it so. If she's got no interest, tell him to keep it in his pants and find his own girlfriend. If he wants to add a unicorn to the relationship, it has to be done consensually.
Sorry if this sounds ranty, but male privilege has been on my mind a lot lately, especially when I see the forums full of unicorn-hunting posts.
"Wish for others what you wish for yourself" ~ A man with many wives. Oddly enough, his wives did not have multiple husbands.