IN my interview group, someone had their father along with them. He sat out in the lobby of the building whenever the applicant was in the fishbowl.
He came along for the tour, but did not talk, just stayed in the background.
Some folks think it is inappropriate, since we are at a professional interview, but I looked at it as one of the most important decisions you could be making, and having someone you trust along couldn't hurt, like a second opinion.
So yes, it is possible, but I would definetly make sure the parent knows they are not the ones asking questions, etc. You don't want it to come across as you can't make your own decisons.
Hope that helps,
Marcia