For SharePoint Server web applications running on Windows Authentication there is only one (very not recommended way) ... use basic authentication for the specific zone. The client will send username and password in cleartext (yes through a secure channel as it is HTTPS, but it is cleartext at the server side). Using sharepoint code running on the server (webpart, application page, ...) you would be able to provide the needed information. The other information might come from active directory (LDAP query) or from user profile service. Other windows integrated authentication mechanism will not transport the password, so it is not possible to extract the password(, if not stored in an excel file on the admins desktop ;-).
For SharePoint Server running the web application using forms based authentication, it is depending on the custom authentication provider an the way passwords are stored. It might be possible to extract the password out of a sql membership database... and get the other info's from here to.
If password is not needed Eric has provided you with a valid option.
ATTENTION: I DO NOT (I DO NOT (NO I DON'T)) RECOMMEND THE TRANSPORT OF THE PASSWORD IN THE URL EVEN OVER HTTPS. THIS IS A BAD PRACTICE.
With SharePoint 2010 claims based authentication based on industry standard are available to solve this kind of problems... only problem 3rd party vendors are not jumping the claims auth bandwagon.
Another way to improve your situation is to include not the password, but an information only available to the involved servers so the user is not able to fake the authentication. Think of a has with a shared secret... more more crypto related stuff.