As you've noticed, you might be able to channel the audio from your soures directly to your audio system but there's no way to connect any tv audio out to it.
Like many modern TVs, your set has a plethora of inputs but, alas, it sorely lacks in audio outputs. Without them, you're out of luck in getting your TV sound through your audio system.
But, if your TV has a headphone jack you might be able to do it or, if it has digital outputs you should be able to do it with an external adaptor. Does it bave either?