The integration that we have implemented with phpbb is very custom and specific to our needs. The implementation took a bit of planning and many hours of customization to get it the way we needed it because of our requirements.
I would suggest that you start by looking through some postings on integrations to see if you can find any that are similar to your needs and try to work with that. To get it all worked out though will require you to do a bit of custom dev work to integrate things.
I just wanted to update this post to clarify that the system we use is the vBulletin one.