https site redirection to default page

[bshbsh]

This is strange as it has never happened before. I have a site for which I installed a web certificate. I left both 80 and 443 open. To browse visa http, I open a browser and type in the following URL,

http://site.com

and it automatically redirects to

http://site.com/default.aspx

But when I type

https://site.com,

it does not redirect me to

https://site.com/default.aspx.

I have to type in the entire thing. I checked IIS and the only file listed as the default document if default.aspx.
It doesn't help even if I enforce SSL on all connections.

IIS 6 on Windows 2003 Ent.

Please advice.
Thanks.