Two Websites, One IP - Can't Authenticate Properly

I have two websites:

www.website1.com

www.website2.com

I have two Internet Site documents:

For website1:

The field “Hostname or addresses mapped to this site” = the single IP address…xx.xx.xx.xx

For website2, this field is set to www.website2.com.

When using Domain Details Page and attempting to edit a web document, I can’t authenticate unless I change the the URL to www.website1.com/database.nsf. Why is this?

These websites are two divisions in the same company, so I need each URL to remain and also be able to authenticate regardless of which website I’m using.

Thanks.