Sounds like unregistered or not logged in users don't have ANY permissions on the subsite, which means they're not allowed to SEE the login page. (I've done that one too.) You probably want to give The Public read privs on the subsite itself (so that they can log in), and then remove or don't inherit it on mounted packages.
(If you don't want them see even that first page, check that they're logged in and redirect them to the login screen if they aren't, or modify the content displayed.)
HTH
