Relationship(?) Advice

My fiancée and I are kind of in an argument right now. I’m my system’s host so I’m most active and the one he associates most with our body. One of my now conscious head mates is a lesbian. She was super excited to make friends and maybe even fall in love. My fiancée wants nothing to do with this. He basically set the boundary of “she can date me or date no one” as if I and her are the same. We obviously aren’t and I keep asking him to treat all the members of my system as real people and not just “other flavors” of me. Any advice on what to say or do? I really don’t want us to break up over this but it’s clear this issue isn’t going to be resolved anytime soon.