I'm not sure there is an easy solution to get all three working together. (I've tried).
However I think there is a way to get Joomla and phpbb to link accounts, so creating an account on Joomla will create an account with the same username/password on phpBB, there is an extension for this somewhere.
The best option would be to use Google to see if someone has come up with a way to do it. Also make sure you look through the Joomla extension database.