(somehow, every manual I find for this set on line is in French which does me no good)
Great! Since you can set it's output to either, pick one and get hold of one of these:
This one does Dolby Digital.
This one does PCM.
You can get an RCA cable to connect it to your TV at your local Radio Shack, Home Depot or even Walmart. You don't need anything fancy. Virtually any should do.
Then, connect your headphones transmitter to whichever device you wind up with.
Happy listening, and sleeping.
And, another marriage saved by markw.
[edit] I'm not sure how or if the TV's volume control affects the digital output. Hopefully, the digital output is independent of the volume control. You might want to check this out.
You don't use a cable box on that TV?