Well, there is no straightforward way to do this since the computers cannot communicate with each other. But you can try this:
one of you exports the database to a website and the other one then clicks on the little blue sharing icon on the webpage. (On most templates this is located right next to the title header.)
This will download the database to your friends DVDpedia and create a shared collection (with a special shared collection icon) so you can both see the same database. To update the shared collection, your friend simply has to select it and choose 'Update shared collection' from the File menu.
The one drawback to this solution is that shared collections cannot be edited by anyone sharing it from your website. You will be the only one who can make changes to the database.