RobotC should have no problems with .h files; however if you have definitions, variables, functions, motors, etc., that are referenced in the header then when you open the header file alone you will get errors because the RobotC compiler doesn't know enough to go and look in the main program file because it isn't (and can't be) "included" in the header.
Unlike some well established IDEs (*hem* Visual Studio *hem* *hem* NetBeans *hem*), RobotC doesn't have the idea of a "project" file that keeps track of all the files in your project and thus knows where all of your definitions are, avoiding such errors; rather it leaves you to create the files by hand and only looks in the current file and includes for definitions. RobotC also FOOLISHLY
compiles the program when you open it (find me an established IDE that does this and I will eat my heart out); so that's also why you get errors left in right when dealing with includes.
Just be sure to avoid circular includes and stick to the 14 file limit and you should be fine.