This is likely a school specific issue. I know of at least 3 schools that allow you to pursue more than 1 curriculum in graduate school. I imagine there are more if you look.
Furthermore, there are schools that, in addition to allowing more than 1 curriculum, allow you to have more than 1 concentration. Of course, there are procedures and approvals required, and it's most likely to apply to MS rather than Ph.D for reasons stated by chiro and eri.
http://www.grad.illinois.edu/petitioninstructions
In the case of Ph.D, if your interdisciplinary study is not too obscure, chances are, the other department has faculty that is part of your own department's affiliated graduate faculty. That way, you remain in your department, but your advisor is in another department. Ph.D is when you narrow down your area and become the expert and is no longer where you divide your time trying to be the jack of all trades like undergrad.