“Allows Parent to be specified” means that the post type behaves more like pages than posts.
What you are trying to achieve is not possible with core functions, but there’s a plugin wich does almost the same.
I recommend you the powerful Posts 2 Posts plugin by WordPress Core Contributor scribu. It allows you to create connections between different post types and has lots of configuration possibilities. The screenshots and the documentation can give you an impression if it’s right for your task.