When my best friend and I are alone, we will lightheartedly refer to our significant others as "my person".
My mom usually refers to my boyfriend by name, but she never says "your boyfriend". She always says "your sweetheart".
My Filipino aunts always call him my "special friend"
I will sometimes refer to him as my man. Or manfriend, but that's usually when I'm being a little silly.
I've heard from mutual friends that he has referred to me as his lady in my absence. I think it's sweet.
I agree with Rachel that "my boo" isn't appealing, but I don't mind "beau".
Also, I don't like the term "my honey". I don't know why. It just makes me cringe. It's not the same as calling someone "honey" directly. But referring to them in the third person as "my honey" weirds me out for some reason