DVI i believe is video only. From my understanding, having both audio and video in one cable was one of the huge benifits for TV manufactures adopting HDMI in the first place.
There is an audio limitation to it though, which is where people may be getting confused. I believe the 360's HDMI is capable of carrying DD/DTS, but is NOT capable of carrying multichannel PCM. This only really matters for HD-DVD though...