Can a custom post type have a Parent Page?

I’ve seen a lot of posts out there in the Webiverse about assigning a page as a parent of a custom post type. After four hours I can’t find a solution and need some help. I’ve create an “About” page that is the parent of an “Our People” page. I’ve also create a custom post type called “People”. And I’ve created a custom page template for the “Our People” page. The Permalink structure looks fine until you get to the single “people” page. For Example: John Smith’s Page, the permalink isn’t correct.