Well, I've always kind of wondered this, too. On the face of it, the two are completely unrelated. Suppose you turned the higgs field off. Never mind how you'd do this, but just assume that you could. Most of the matter in the universe would still have mass. The proton and the neutron, for example, don't need the higgs to be massive. And dark matter would probably still be massive, too. So this tells me that the higgs has absolutely no relationship to gravity. That is, gravity still exists if there is no higgs.
I think that the correct statement about gravity is that it couples to energy density, not mass---this is literally what the Einstein equations say. I guess that ``energy density'' sometimes just means ``mass''.
But this is a bit of a cop out: I've just pushed the question about the higgs back to a question about whatever gives the protons and neutrons and dark matter mass :) Suppose you could somehow switch off ALL mass in the universe, and protons and neutrons were massless. But this stuff STILL couples to gravity, because it STILL has energy---in this case, the massless stuff would have kinetic energy.
This answer is right, I'm pretty sure, but it doesn't help me sleep at night, so to speak.
