I'm probably just going to muddy the waters here. I have a few systems connected similarly and have no trouble. In my living room I have a cable tv digital box with the analogue rca red and white audio outputs connected to an analogue stereo. There is a third yellow rca output with video that I am not using. There is also an HDMI output that goes thru an HDMI cable to the tv. The hdmi cable provides the video and audio to the tv. I turn down the tv audio to listen thru the stereo. It works fine.
I use the same set up in the rec room. I use a similar set up at my cabin with a satellite hd pvr. All three of these hd tvs are Samsung. I guess the audio quality is dependent on the programming and the circuitry in "the box". I connect my dvd players using the three rca connections (ie yellow video to tv and red and white audio to the stereo). If I use the HDMI connection I get sound only thru the HDMI cable and miss out on using the analogue audio to the stereo. I guess that part is either/or but not both.

If you are taking audio out from your TV, I'd recommend spliting your aduio out of your cable box, (sat dish, Blu Ray, etc). Sending one path to the stereo the other to the TV.

Or as posted above, take the analog RCA jack outputs to your receiver and HDMI to you TV. Turn the sound to zero on your TV when listening thru the stereo.

That is assuming that you aren't using a surround sound receiver. If your receiver is surround sound, use digital patch cables. I'd recomment COAX or Digital Optical from the source to the receiver.

There is a reason to not do this if you have traditional vintage speakers. Todays movies DVD's have sub bass intended for sub woofer modern systems. Think earthquake type effects. It is so low a frequency it exceeds the bottom end of vintage speakers and at higher volumes can damage the bass speakers. I keep my vintage system separate from the TV and movies, you can get an OK sound bar if you do not want mirror systems.

I'm probably just going to muddy the waters here. I have a few systems connected similarly and have no trouble. In my living room I have a cable tv digital box with the analogue rca red and white audio outputs connected to an analogue stereo. There is a third yellow rca output with video that I am not using. There is also an HDMI output that goes thru an HDMI cable to the tv. The hdmi cable provides the video and audio to the tv. I turn down the tv audio to listen thru the stereo. It works fine.
I use the same set up in the rec room. I use a similar set up at my cabin with a satellite hd pvr. All three of these hd tvs are Samsung. I guess the audio quality is dependent on the programming and the circuitry in "the box". I connect my dvd players using the three rca connections (ie yellow video to tv and red and white audio to the stereo). If I use the HDMI connection I get sound only thru the HDMI cable and miss out on using the analogue audio to the stereo. I guess that part is either/or but not both.

Umm, could I buy some pot from you?