Well, I don't really know, but I spent some nights in austrian huts a couple of years ago. We were all members of the FEDME (spanish federation for mountain sports and climbing, associated to the UIAA) and discounts were strictly personal. I mean: one membership, one discount. I guess your situation would be kind of similar, as far as the American Alpine Club is also associated to the UIAA. Maybe ask them?
One other piece of information, you might like to know that some austrian huts are managed by sections of the Austrian Alpine Club (ÖAV) while others are managed by the German Alpine Club (DAV). I don't think it makes any difference, but just in case...