Right now I am finishing the math to prove a new theory as to the nature of space and time. I think this theory can answer your question quite nicely, allow me to explain.

You wonder if absolutely nothing exists between two objects. The question seems to be is space itself nothing, and if it is, then why does matter obey a certain set of laws? Space then, must not be nothing, due to the fact that the continuum dictates the laws that matter obeys.

The question itself "does nothing exist?" is not all that valid. You wonder if anything exists between you and an object, right? That question, and they idea of space itself, is based on the assumption that you and that object exist simulateaneously at all.

Look far away across the room, at an object whose motion is at rest with respect to you. Now without changing the way in which either you or the object travel through time (according to einsteinian relativity changing velocity will accomplish this) touch the object. You can't can you? Infact without changing the way in which either you or the object travel through time, you cannot affect this object at all. Now, are you sure that both you and the object exist at the simultaneously? I don't want to completely reveal my beliefs as to the nature of space and time yet, I will soon when I copyright them, but this is truly something to think about.