It might be incredibly insane to do this, and your ISP may block it, but I don't see any reason why you couldn't host a fileshare over the internet. The other party would have to do \\yourIpaddress\share . That *might* work.
EDIT: You would need Win2k/XP which supports port 445 NetBIOS connections. If you have a router, youd have to forward port 445 to your PC.