You'd have to use a STB or Blu-ray player with both HDMI and analog (S-video in my case) outputs. For my audio-only source (Squeezebox), I simply assign the Blu-ray's S-video output to it, so I can listen to music while playing video off the player. You could do the same thing with a STB if you just want to watch TV.
The downside is the video is going to be of lower quality than HDMI. So it's not a good solution for the PS3 fellow above. But decent enough if you just need casual viewing.
I realize this is an old post, but I have struggled with this problem for over 2 years with my Denon AVR-2112. I finally figured out how to do this today! Thought I would share my options and results.
There are actually 2 ways to get it done. Both involve using the V-Aux inputs.
Option 1 - Shows Analog Video and Analog Audio on your screen/speakers
Plug the video out from your cable box to the v-aux video
On CD - Set Video Source to "V-Aux"
I believe this is a commonly known solution using the Video Source over the CD input...
But this is a bummer because I wanted the HDMI signal from my DVR on the screen and listen to CD/Computer sound but Video Source didn't allow for digital video sources on my Denon.
Option 2 - Setup V-Aux as follows:
In source setup, Choose HDMI 3 (or whatever your Sat/Cbl DVR is plugged into on your receiver)
Make sure to choose Analog / RCA audio as well
Plug the CD/Audio Source RCA cables into V-Aux audio plugs (Not a huge loss for me since CD seems pretty useless)
When on the V-AUX, go to Source Setup Audio Settings and tell the receiver it to play analog source and not digital sound
This worked! It plays digital video from HDMI 3 while playing audio from the RCA plugs. I can now play my DVR HD quality video on my screen while listening to music/computer/cd. Something I have been trying to do for years. I have seen on many discussion threads on this but never a clear solution that I was able to follow.
This was NOT INTUITIVE for a novice like myself! What should have happened was on the Source Setup for V-Aux, I should be able to choose HDMI for video and CD for sound, but they fail to provide audio as one of the options.
Note: I believe it only works to play ANALOG audio with DIGITAL video (Option 2 above)
Analog Video with your CD (Option 1 above)
I haven't tried to play Digital audio over a different Digital Video but this might be possible too. I don't have digital coming from my Computer at the moment so I can't test.