Is there a way to upload files other than media to a website in 4.0.4?

[AC Question]

When I try to upload a data file to a website the File Upload screen appears but the only choices are Camcorder,Camera,Gallery,Music Player. I need to be able to navigate storage to choose a local file. Can this be done? I've tried Firefox and Chrome browsers and I get the same result so I figure its an Android constraint.

 

[B. Diddy]

Welcome to Android Central! Which website, and what kind of file?