One of the benefits of the PhD at IU is the requirement across campus to obtain a minor. This requirement forces doctoral students to gain competency in a discipline tangentially related to their own primary program discipline. It is very useful to mix foci in this way to increase in breadth and depth of understanding with respect to your particular research interests.
Another aspect of cross-department work is the networking that takes place as a result. Some of my favorite professors have been those from other programs–both from my minor and from methods courses. Additionally, at the level of students, working with students of other departments and disciplines has been beneficial if not enjoyable. Comparing programs and experiences is one way to gain insight as well as stay sane. For me, it has been very healthy to hear what is working for my peers in other programs and disciplines. I highly recommend cross-pollinating your studies and work experiences in this way.
(Also, as a side logistical note, there are IU-sponsored technologies available if you would like to collaborate electronically.)