Drupal 6: CCK Images broken (because of path) on multisite after copying/moving site
Changing site URL with a multi-site setup in Drupal 6 is problematic as the paths in the file table will be incorrect.  (See Migration failed)

In Drupal 7, you set up multi-site aliasing via the sites.php file (copy and edit the existing examples.sites.php),  which should be stored in the /sites directory.  

For Drupal 6 you can try applying the multi-site aliasing patch.

As a last ditch effort (not best practice) you can also try editing the database (e.g. system and files tables) to change the file paths to reflect the new path.