NationBuilder allows you to store files like PDFs and images on a directory assigned to each page. You can also store files such as MP3s under the files director of a custom theme.

If you want to link publicly to a stored file, do so by right clicking on them and copying the link, then making it the hyperlink in the public pages. Your files each have their own URL that can be linked to on public pages. And if you want to make it so they automatically download when clicked, here are the instructions for that - http://www.wikihow.com/Make-a-File-Downloadable-from-Your-Website.