I have a European Rock Band disc and purchased U.S. downloadable content (or vice versa). Will it work with my game?

You should make sure to buy downloadable content that is the same region as your disc and your console, as these may not be cross-region compatible. You can check with your console's customer support (Microsoft, Nintendo, or Sony) to find out more about cross-region compatibility, but in general keeping everything in the same region is your best bet. That way you can sidestep any region compatibility problems altogether!