Yes, you can definitely make it so the links that a customer clicks on will take them to the non secure part of the site. To do this you just need to specify the full address to the page. For example in your navigation if you use the full address for the home page like this:
index.php
This will force it to work with the regular http version of the page. The reason you are getting to secure versions of the pages after using this code is because the links are relative. This means that they will use the same protocol and port as the page they are currently on.
