Page Template not Working with Posts Page

I’m working on a custom themed site, and I’ve set it up so the main page is static, and the posts page is separate.
I’ve created templates for all the pages, and 4 of the 5 display perfectly. I’m having problems, though, with the posts page. It displays all the right styling, but there is no content within the <content> tags other than the blog posts. I have applied a template to this page with other content (that worked fine with all the other regular pages), but it seems that WP ignores templates on the posts page. Why is this, and how can I change it/work around it?

Please let me know if I can clarify in any way.