What role do professors on a graduate student's PhD committee serve? Do they discuss the graduate student in meetings with each other? Or do they have any obligations to interact with the graduate student in other ways?
I think the variations here are national rather than by discipline. 

In the U.S., the thesis committee's primary role is that of a review panel when all is going well, and as a neutral arbiter between student and advisor when it isn't. Again, there is no formal obligation on the part of the committee—except when convened by the student or advisor, but this typically occurs on a more frequent basis (every one to two years or so). As individuals, however, committee members may be consulted with on various topics (job placement and career strategies, suggestions for future research directions, and so on); however, this is voluntary and, again, not very frequent—probably one or two times per year.

In Germany, by comparison, the primary obligation occurs at the time of the thesis defense, when they serve as evaluators. Outside of this, you might never meet with the professors on your committee, other  than your primary advisor.