Multi-site setup outside public_html and add on domains
By the definition of multi-site: you use one Drupal installation (core) to host several sites. But according to your problem, you want a separate instance of Drupal installation and hence it's considered a "multi-site". 

You need edit your virtual host file and point http://assitertselvh.no to the specific folder you're hosting to:

Please use the following guide to edit your virtual host.

http://drupal.org/node/111238