I can do it with FileMaker 11 on WindowsXP. Here's a demo file: http://www.4shared.com/file/5_bRPbKu/MultiFieldLookupTest.html
(Click the blue download button, wait for the 20 second countdown to finish, then click DownLoad Now.)
Compare it to yours and see what's different.
By reviewing your sample, I was able to figure out what was going on.
Eventhough the relationships were defined, and all the fields showed as lookups in the table design, they'd "forgotten" where to go to lookup the data. I had to edit them all, but one I did it worked as expected.