Computer science is a discipline that is intrinsically interdisciplinary. Primarily because the computer itself—the externalization of our logic apparatus—is such an enticing and versatile tool. Therefore, it is not hard to find examples of cross-disciplinary approaches. Just think of Artificial Intelligence and all the areas it draws upon. A less well-known example is the subject of Artificial Immune Systems (AIS) in which I've done some work. Here, computer scientists and immunologists are collaborating to, among other things, learn nature's algorithms for defending the body against pathogens and apply them as another security paradigm to other areas—anomaly detection systems for networks as PCs, data protection schemes, and so forth. It remains to be seen if the road can be traveled in both directions and computer science (AIS) can inform questions about the natural immune system, it will be surprising if it can't.
The last part of the question is hard for me to answer without engaging in platitudes: Cross-disciplinary approaches are not appropriate when they are expected to bog down research; when they are forced upon; when they obfuscate ethical boundaries. There is no a-priori reason pertaining specifically to cross-disciplinary research that can be cited to avoid engaging in it. The main benefit of collaborating with people with other areas of expertise is the compulsion of viewing a problem from a different perspective; this usually increases the understanding of the issues at hand and the understanding of our understanding, which is, more often than not, a good thing.
And I ended up with an Information Science degree. It was heavy on database courses.