grammatical number - What is the proper way to say possesive with "person X" and self?

I've never known what the proper way to use a sentence in which you and a specific person (as in you can't just say "our" because you want to specify who) possess something. Is it "Julie's and mine", "Mine and Julies", "Julie and my"...?

For instance,
"Julie and my favorite band is Eluveitie."
"That sandwich is Ben and mine."

They all sound a bit strange, which is the correct way to say this?

Answer

"Julie's and mine" and "mine and Julie's" (note apostrophe) are both correct for the predicate possessive form, "Julie's and my" for the simple possessive form.