Prince Jackson clearly knows how to compartmentalize his life ... because he hit the town Tuesday night in low fashion, attending the premiere of True Blood, Season 6.

The 16-year-old and his GF, Remi Alfalah, were flanked by 3 bodyguards as they left the ArcLight in Hollywood. 

People inside the screening tell us ... they were "touchy-feely" and seemed happy.   Almost everyone was dressed up -- except Prince, which either makes him a slouch or a baller.

Prince seemed annoyed when photogs asked him about his sister, Paris ... specifically how he felt about the possibility that Debbie Rowe could become her guardian.