I went through my undergraduate studies with a triple major - at least one humanity (philosophy) and at least one science (physics). I'd call mathematics a very fine art myself, but describing myself as a fine arts major would lead to no small amount of confusion.
I've been describing myself mainly as cross-disciplinary; the reason is that if I said "interdisciplinary," I might be confused with an "interdisciplinary studies" major. The field of interdisciplinary studies seems to be a very specific one now, and while I've had a good measure of respect for some such programs, I clearly wasn't part of that particular sort of program.
The very notion of disciplines does mean that problems that cross over the boundaries of traditional disciplines are in an odd spot - perhaps under-studied when they require the tools of both disciplines, perhaps simply subject to poor communication and turf wars when the traditional tools of both disciplines work well on them.
But oh, though the lines are blurry, how useful it is to have separate departments, and so clearly communicate where most of the specialties go!