A surprising number of the old Portland theaters serve beer and food. The one I've been to (haven't visited them all) that serves you at your seat is McMenamin's Mission Theater at 16th and Glisan. I haven't been to Living Room Theaters on 10th, but they serve you at your seat, just not while the show is in progress.
The only McMenamin's theater I've been to is Kennedy school, might have to try out the Mission Theater, will have to look into the Living Room. Also, the Hollywood Theater on Sandy now serves beer, but they only show indie films, so I haven't gotten my wife to go there yet.
