I've got the Audible.com application on my smartphone. So in theory I could play the audiobook version on my smartphone while I'm reading the e-book version on my Kindle.
I'm not sure why Amazon doesn't let you read while you're listening to an audiobook on the Kindle. Maybe they just never got around to programming it yet. Plus, I bet it's a feature that they'll have available within a few years. Amazon's just now getting around to promoting audiobooks more heavily. Audio (and video) will be a big part of any iPad-style tablet that Amazon wants to release.
At that point, they'll start taking audiobooks more seriously - and when people start using them more, Amazon will start adding more features to the Kindle for audio playback.