OP, an added option to the above replies would be to insert a middleman component- a receiver or amplifier "box"- which will then give you the fuller compatibility to do all kinds of things not walled garden. In other words, think about the signals of video & audio like they are tangible entities. Once they escape the AppleTV and are inside of a receiver or amplifier, they are fully outside the walled garden and will be able to do anything within the capabilities of the device. Those signals are delivered to that device as full & complete as possible... just outside of Apple decision-making (for us) control.
At least one more option that this would open up is wired headphones, which would overcome all limitations & shortcomings of pinched-bandwidth Bluetooth while delivering the fullest quality of the source to your ears. For example, if you would like to listen to Apple Lossless audio to its fullest, there's not enough bandwidth to do that with bluetooth-based buds & phones. However, good old wired can deliver.
If the only thing you want to do is listen with buds, a receiver or amp would be overkill unless perhaps you already have one (if so, dig into it to see what it can do for you in this direction). However, especially a receiver as middleman between AppleTV and TV really opens up a LOT of ways to improve a watching & listening experience... which includes much more flexibility with various kinds/brands of headphones and buds, wired & wireless.
