restricted areas

You can password protect certain pages with the build in WordPress feature.

You;re right, the built in option is a very simple one and wouldn’t work that way.

I’m not familiar with membership plugins, but these do exist.
Check out these plugins – http://wordpress.org/extend/plugins/search.php?q=members&sort=

and here’s a review of some other ones.
http://tomuse.com/wordpress-membership-plugin/

Perhaps one of these will work.