The rising popularity of digital table surfaces has spawned considerable interest in new interaction techniques. Most interactions fall into one of two modalities: 1) direct touch and multi-touch (by hand and by tangibles) directly on the surface, and 2) hand gestures above the surface. The limitation is that these two modalities ignore the rich interaction space between them. To move beyond this limitation, we first contribute a unification of these discrete interaction modalities called the continuous interaction space. The idea is that many interaction techniques can be developed that go beyond these two modalities, where they can leverage the space between them. That is, we believe that the underlying system should treat the space on and above the surface as a continuum, where a person can use touch, gestures, and tangibles anywhere in the space and naturally move between them. Our second contribution illustrates this, where we introduce a variety of interaction categories that exploit the space between these modalities. For example, with our Extended Continuous Gestures category, a person can start an interaction with a direct touch and drag, then naturally lift off the surface and continue their drag with a hand gesture over the surface. For each interaction category, we implement an example (or use prior work) that illustrates how that technique can be applied. In summary, our primary contribution is to broaden the design space of interaction techniques for digital surfaces, where we populate the continuous interaction space both with concepts and examples that emerge from considering this space as a continuum.