Lots of confusion here. First, DVI is video only. if you have DVI in the chain, then no audio.
Also, just because a home theater receiver has HDMI jacks on it, that doesn't necessarily mean that it will decode audio from the HDMI cable. In fact, most lower-cost receivers won't, they simply act as an HDMI switch, so you'll always need a 2nd cable for the digital audio (co-ax or optical). That is one of the things that sets apart the Onkyo TX-SR605 from the TX-SR505. The less expensive 505 only switches HDMI sources, while the more expensive 605 can do that and decode audio, too. At $600, many consider the TX-SR605 a bargain. If you find the store section on the Onkyo website, they have a factory-refurb (same warranty as new) for $400, and sometimes, you can get it for $340!
I guess the moral of the story here is not to assume that just because equipment has HDMI ports, it will properly handle multi-channel sound.