Recently, I got around to seeing the movie Interstellar. In it, the characters of the movie visit a stellar system that appears to be built around a black hole instead of a star. On top of this, their mission is to find a habitable planet in this system. I was wondering how stable the system, as a whole, would be in terms of operation and would any of the planets be habitable at all due to the obvious differences between a star and a black hole.
In the movie the black hole is supposed to be a 'supermassive rotating black hole'. As for being a binary star system, it's never stated as such nor depicted as such. It's depicted visually as the black hole alone being the center. However one of the characters does mention a "Neutron Star" as part of the system so it could possibly be a binary star system. The ambient lighting for the planets is generated by the accretion disk of the black hole. The size and rotation speed of the event horizon are not defined in the movie. At least not that I can remember.
As for the planets, their proximity varies, with the first planet depicted as being so close to the event horizon that it is effected by time dilation. The distances of the other two are not specified directly, but traveling to the second planet out seemingly takes days, while traveling to the third planet out is stated to take months, if I remember correctly. As for their surface gravity, the first planet is depicted as having higher surface gravity than Earth but not so much higher that movement is impossible, just strained. The second planet is depicted as being '80% Earth's gravity', if memory serves me correctly.
To better help define certain variables relevant to the question I found an info-graphic related to the movie that illustrates the size of the black hole and it's rotational speed: http://tinyurl.com/pqph8wl