IIS 6, Windows Authentication and Terminal Server

Hi,
Been searching this forum and found the same question before, but no
straight answer on how to solve the following problem:

When accessing a website on IIS6 (Windows Authentication only) through
a Terminal Server session I will always get prompted to log on to the
domain, even if I'm using local URL's (like http://myIIS/default.asp).
The account used to log on to the Terminal Server (we can call this
user TSUSER1) will have access to the site if logged on to the network,
so there's nothing wrong with the security settings on the IIS.

When connecting through TS I notice that the TS thinks I'm trying to
connect to the site with a full URL
(http://myIIS.mydomain.local/default.asp) even if I'm using the local
URL in IE (http://myIIS/default.asp).

Is this normal behaviour when using TS, or am I doing something wrong
here?

Regards,
Bjorn