When you create a new mailing the help text for Mailing Visibility says:
""user and user admin" only means that only users that received the mailing or administrators can view the content of this email as a web page; the recipients will have to log in to be able to view the message"
However that isn't what happens. If you set the visibility to " User and User Admin only" logged in users receive an "Access denied" message when they click on the URL to view a mailing in their browser. You have to give them the access Civimail before they can view the mailing. This also gives them the ability to create emails, modify mailier settings etc which is definitely not appropriate.
This effectively means that the visibility has to be set to "Public Pages" which means there is no such thing as a member-only newsletter.