Problem with redirecting home directory to subfolder

Greetings,
I am having a following problem. I made a redirection using IIS, by
changing the settings of the Default Web Site (Properties -> Home
Directory; there 'A redirection to a URL' and 'A directory below this
one' have been selected). The problem is that when I am physically on
the machine where the server is running and type in the browser
address bar http://localhost I am indeed redirected to
http://localhost/subfolder/Start.aspx - this address occurs in the
browser's address bar. But when I do it using the domain name the
redirection occurs and a file Start.htm containing a line
window.open('Start.aspx','_self','',true) is found. That is ok. But
then the address which occurs in the address bar is http://mydomainname.com/Start.aspx
instead of http://mydomainname.com/subfolder/Start.aspx. This results
in the 404 site not found error.
I would appreciate any ideas/suggestions/explanations.

Best regards,
Piotr.