Simultaneous independence/interdependence of the hands is certainly possible. Until it becomes second nature, I can think of a couple things that may help.
Try playing passages in which both hands are playing the same notes in unison but one or two octaves apart. (Hanon exercises are a good example, though I'm sure you can find, or improvise, more musical ones.) When the movements are identical and synchronized in this fashion, you may find it easier to focus on your image of each hand individually and your mental connection to it.
Another strategy might be to practice HS, and then incrementally add the notes played by the other hand. While practicing the right hand's part, for example, include only the left hand's notes that fall on, say, the first beat of each measure. Then reverse the exercise, letting your right hand drop in the occasional notes while the left hand plays continuously. The pattern or frequency of gradually appending the opposite hand's notes is up to you; experiment to find what yields the best results.