Hopefully I will be able to clarify this to you.
The between and makes perfect sense if you look at the verb as you would look at a modifier/adjective.
Few examples:
- book that was bought - letter that was written - child that is running
Even though, you're using a verb, it acts and modifies the noun as an adjective, that's why you can treat it as a noun phrase.
Hopefully you got it by now. If you need some more help, let me know :)