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.
Desktop machine: 2 x Opteron 246, Asus K8N-DL, 2GB PC3200 ECC Reg., XFX GeForce 6600GT, 74gb WD Raptor, 2 x 19\" LCDs, Windows XP x64
Server machine: Intel P4 3.0GHz 2MB EM64T, ECS i865pe, 1GB PC3200, 36gb WD Raptor, Windows Server 2003
Laptop: Dell Inspiron 9100 (Intel P4 3.2GHz 1MB Prescott, i865pe, 512MB PC3200, Mobility Radeon 9700, DVD+R/DL Burner), Windows XP
Linux: P3 450Mhz, 386MB ram, Slackware 10.1 (Running mySQL/Apache)