We need a new word.
My niece is living with a guy who I'll call Kenny. They aren't married, but have a child. They plan to spend the rest of their lives together, in a loving and committed relationship. But they aren't ever going to marry. And that's fine. In fact, it's wonderful that they found each other, and I don't care if they ever marry. That's not the point. I absolutely approve of their arrangement. This post isn't about that.
They aren't alone, either. I have a cousin, now in her fifties, who lives exactly like this, and has for years. I suspect this trend will continue, rather that abate.
But here is my question: Kenny is her _________.
Not husband. Then what? Significant Other, I suppose, is fine. But Kenny is part of our family, whether he's married to my niece or not. "Significant Other" isn't something one family member calls another. (I can just see the Christmas card: To Kenny, my niece's Significant Other) Another family member suggested "her man." Really? It's not like they're dating. They live in a house together, committed to each other, raising children. So we need a new word.
Oh, and what does my brother, my niece's father, call Kenny? Not Son-in-Law, because he isn't. We need a new word for that one, too.
= new reply since forum marked as read
They ultimately get to decide what other people call them.
Welcome to the world of non-conformative relationships. 
Isn't that why we name our children?
