On J!1.5.6 with CB1.2RC2, a link on the home page to an article that is otherwise accessible by a menu for registered users brings up Joomla's message "To access the private are of this site, please log in". It also displays a login facility, even though the standard login form is not published.
I believe this is in the language file, english.php, but if they know to log in first, they wouldn't be clicking on the link and getting the message anyway?
I am having the same problem except it is after a session timeout. If I allow the session to time out and then click on anything I get the same symptoms as adrian, 2 login screens.
There is a mambot (plugin) on Joomla extensions site (see CB extensions) that redirects things to from Joomla registration process to CB registration process.