Registration form would need to be changed to target the parent so its post is sent to the parent window instead of it self (iframe). Quick and easy way to do this is to edit the CB template PHP file and to a str_replace to add it. Below for example will do this to the default template (or any CB template using the default.php file which is most).
IN: components\com_comprofiler\plugin\templates\default\default.php
ON: Line 228
FROM:
Code:
echo $this->regFormTag;
TO:
Code:
echo str_replace( 'method="post"', 'method="post" target="_parent"', $this->regFormTag );