Have you, by any chance, set up your file sharing preferences inside the Airport Utility to secure your shared Airport Disk 'With Accounts'? When I tried this, the drive was mapped automatically on both my Macs and I could see how much space was used on the drive, just like you describe, but when I opened the mapped drive I wasn't able to see any files. I suspect this was because I was only able to see the contents of the newly created user folder that was added to my Airport Disk to match up with the user account I had specified in my Airport Utility. Have you tried changing your Airport Utility's file sharing configuration to secure shared disks 'With a Disk Password' or 'With Base Station Password'? That's what I had to do to enable me to see the contents of the other folders already existing on the drive.