This drives me absolutely crazy and I'm hearing it often from intelligent people.
"Greg and I's relationship."
Should it not be the following:
"Greg's and my relationship"
Am I wrong?
"Greg's and my relationship" is preferable to "Greg and I's relationship" (which is wrong).
"Mine and Greg's relationship" is the best way to say it.
Here's a quick lesson joint ownership with apostrophes. (It's at the very bottom of the page.)