The separation of the Hulk and Banner varies in Marvel comics. Sometimes, external forces or internal conflicts cause them to split, but it's not a consistent occurrence throughout all comics.
Yes, there are some hints of a special relationship between them. In the movies and comics, they share a unique bond. Hulk seems to have a certain level of protectiveness towards Black Widow, and she is one of the few who can somewhat reach out to the Hulk within Bruce Banner.