They can't party with you in any PF that you put together or that they put together. They can still party with you if neither of you is the party leader.

An odd quirk of the current functionality is that you can still be matched with them in Duty Finder, but you won't be able to see anything they say in /p chat. There won't be any indication of this, and your blacklist is not available during a duty, so you won't know unless you have a friend with you who can see the other person's chat or if the party members you don't have blisted look like they're talking to themselves.