You are attempting to mount the backup from the Vista machine on the Windows 7 machine, and you're running Windows 7 build 7000, right? If so this is a known issue with this particular build of Windows 7. It worked correctly in builds prior to build 7000, and I'm told works correctly with builds after 7000.
The best advice I can give you is to try to borrow some other computer to do the single file restore.
I'm not on the WHS team, I just post a lot. :)