I haven't used chessbase yet, but I imagine you should be able to save the puzzles as pgn files and then combine them. Here is an old video I found on combining multiple pgn files into one if it's helpful (uses Windows command prompt but seems to be a nice solution--I'm guessing there are other ways to do this too).
How to save my collections of tactical puzzle
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Hi guys, how to safe a collection of chess puzzle..what software do you use and how you use it. I want to save 1001 chess combinations and 80 classic chess problem. And how to share it online, javascript? how?..btw I got chessbase 11