If you click Reply at the bottom of the thread, and not use the Quick Reply box, you'll get a different set of options. If you see the two rows of Smileys, you're in the right place.
From there, you can click Additional Options, and you can upload your files from there.
Keep in mind, there's an undocumented limit to file size... It's approx. 1.5mb in size, so anything larger needs to be compressed or broken into bits and pieces.