At the moment there doesn't seem to be an easily identifiable method of moving from the private area back to public area. In the Private area the "Home" link on the top menu bar takes you to the Homepage of the private area (the same applies if you click the logo in the top lefthand corner).
In a similar way that you get the "Private Area" appearing in the top menu bar once you have logged in, is there a way of having a similar link once in the Private Area to take members back to the Public Area. Even if you log out, it doesn't revert to the public area, the system simply invites you to log in (with a login screen).
Good points, we could certainly make this clearer!
In the Bootstrap theme that you're using, the breadcrumb does allow a way out - the first item in the breadcrumb trail is the public site, second item should be the private area, then third item will be where you are within the private area. Though I accept that this isn't very clear (and may vary from theme to theme), and isn't consistent with the links in the main navigation.
Probably a good solution is that when you're in the private area that the main navigation includes the public site as the first link. e.g., "Home" would be first, which would go to the public site, then <name of private area> would be second, then after that all the links inside the private area. Would this make sense to you?
Also I agree that if you log out it should return you to the public pages of the site. I'll also add that to my todo list :-)
Thanks for the feedback