Best bet would be to host the file such that you can connect to it as a client from home. A hosting service can do this or you can set up a computer (perhaps yours?) at your work place to host the data database with "port forwarding" set up to permit you and your coworker to access the hosted database from home.
If you choose to open and modify separate copies of your database, life gets much more complicated. It's possible, but potentially complex to "synch" the data from your separate files producing a copy of the DB with merged data. You might be able to design such a system yourself or there are 3rd parties such as 360Works and SeedCode that offer a tool that can do this.