HDMI and audio?

HDMI carries both video and audio.

the component part carries just video, but there are the usual 2 composite audio ports next to it (a component cable will usually have 3 video and 2 audio connections).

I have my apple tv hooked up through HDMI to my Mitsu DLP TV and the ATV optical output to my receiver. Works great.

HDMI passed through your receiver may or may not work, it is supposed to and in many cases it does but with some receivers it doesn't.

Quite where the fault lies for this I am not so sure, (although it's an HDCP thing and not actually an HDMI thing), in most scenarios I'd say with the source device which is the tv. However since the tv has been shown to pass through some receivers I wouldn't like to say. What makes it more difficult is that in some scenarios DVD players and other devices will pass through a receiver but not the tv. All rather odd I think.

If it doesn't work at first you might find that the order in which you power up the devices makes a difference, I'd tend to power up the delivery device first and the source device last, but all combinations might be worth a try.

One last thing, believe it or not many fail to get the tv to work through a receiver simply because they forget to match the input and output on the receiver.

Not all Sharp TV models pass HDMI audio input on to the optical output. If you have one of those models, you will have to connect the ATV optical audio output directly to your A/V receiver if you're not getting audio passed through your TV and you're not content with listening to it from the TV's speakers.