The Netflix app on the Xbox 360 used to do this. And you and your friends could put on your headsets and watch the same thing on Netflix while chatting.
I was pretty disappointed when they ditched that feature, my friends and I used it pretty extensively as we were all attending different colleges, but still loved to play games and chat online. It was buggy for sure, especially when you added in disparities in lag (which was very common back then).
IIRC Microsoft maintained this functionality however and not Netflix, which is probably why it was eventually discontinued and as far as I can tell Netflix has expressed no interest in making their own similar feature.
Try googling by it's name of "1 vs 100". The game played out where one person was randomly chosen as the main contestant who answered trivia questions. If they failed a question they were booted.
The kicker to the game was, 100 other randomly selected players were playing against you answering the same questions. If they got it wrong, and the contestant got it right they were eliminated and the contestant continued.
The goal of the main contestant was to outlast the 100 players, and the more they outlasted the better prizes (usually MS Points) they won. The goal of the 100 was to outlast the main contestant to also win prizes (usually less than the main).
All other players watching the game could participate for fun and play along for no reward. It was actually pretty fun and the events all happened live with an announcer and everything.
The interface [1] made everything a little better by adding some interactivity. Your Xbox LIVE avatars would sit in front of a movie screen, and you could express simple emotions through them while watching the film. It was actually pretty fun back when the feature was around, especially as high school kids.
I'm glad I'm not the only one to find people talking through a TV show really annoying. I love to chat with people, I even love to chat about things we've watched with them, just not while its on.