What are the benefits and drawbacks of a professor being interdisciplinary when they seek tenure?
If you've been doing interdisciplinary research for five years, and now approach the tenure process without a clear idea of how to sell your case, consider it failed, and start looking for a job elsewhere, before you are under an immense pressure of finding a good job in a one-year grace period after the end of the world as you know it.

If you were hired specifically for interdisciplinary research, and your offer letter stated that, and your time was split "50% + 1 hour in computer science + 25% in department of Roman languages + 25% in agriculture", with a clear explanation as to how you are to be evaluated by each of the parties involved, then these explanations should have served as the guidelines to build your research program. If you were hired to do the theory of parallel computing, but later decided that it would be cool to do some extra work in Roman languages because you liked their research questions, and thought you could contribute with your data mining algorithms that would uncover nuances of how Latin and French are interconnected (and you did, by their standards); and you proposed some GIS tools for horticulturalists to use that have become the industry standard software -- that's all fun and fine, but if you did not discuss that with your CS chair, this was likely a waste of time, as in terms of parallel computing, this time was as good as playing squash. Your annual reviews in the main department should have indicated so, if your department would ever care to guide you (not all departments do, though).

Spending time in another discipline is very fruitful for finding interesting research problems (as typically most disciplines don't talk to one another, and there's a wealth of problems to be solved using other disciplines' tools), but it also means that you have had less time to spend in your home discipline, which nearly inevitably means a weaker CV: fewer grants, fewer publications, lower quality research. (That's essentially Suresh's last point).