Sounds like you guys are looking at doing some sort of distributed source control?
You can set up a repo on github and use git to interface with it, though git is slow working with large binaries, so watch out for that. A number of other solutions exist as well, like perforce, svn, etc.
Just know that binaries are really hard, or impossible to merge, so try and work on non-text files at separate times to avoid conflicts
For more info on Distributed Source Control - Distributed version control - Wikipedia