The black hole was a rotating supermassive Kerr black hole that is rapidly spinning - this was described in the movie as a "gentle singularity." One unique characteristic of this black hole is that its singularity is in the form of a 2 dimensional ring rather than a point - this alters its gravitational properties substantially. Theoretically, one could pass through such a black hole and survive. What happens past the singularity is currently unknown, some have hypothesized that it can act as a portal or wormhole. Here is an article that details their difference as well as explains them mathematically - note they are much different from normally depicted black holes.
http://webcache.googleusercontent.c...lar/comment-page-1/+&cd=3&hl=en&ct=clnk&gl=no
There are a lot of reasons why he may have been spit out near Saturn, such as the wormhole being connected to the black hole in some way. Some theories, as I mentioned above, state that the center of a Kerr black hole can act as a wormhole of some sort. Given its stated that the wormhole and presumably the tesseract were man made, it's not inconceivable that future beings would build it in such a way that it would send Cooper back to the Solar System.