I am looking for a solution to do this, but unzipping the files in javascript was not as clean as I liked. I decided to encapsulate the files into a single SVG file.
If you have the files stored on the server (I don't), you can simply set the href in the SVG.
In my case, I'll convert the files to base64 and embed them in the SVG.
Edit: The SVG worked very well. If you are only going to download the files, ZIP might be better. If you are going to display the files, then SVG seems superior.