The Music Hall unit you have lacks an internal DAC. Thus, you have two options. You can get a headphone to RCA cable and plug it into the back of the Music Hall amp. This will use the internal DAC on the iPhone but will leave you tethered to the unit.

Alternatively, you could get an external DAC like the Peachtree DAC iTx for $299. It would attach to the integrated via a standard RCA cable. You would then run a toslink(optical) cable from an Apple TV into the DAC. You would then connect to the Apple TV via Apple Airplay (not Bluetooth). If you want to connect via Bluetooth, Peachtree and a few other manufacturers make Bluetooth adapters that will plug into a DAC, but last I checked, they were more expensive than an Apple TV.

I personally like the Peachtree DAC very much but if you want an alternative, Cambridge, Schliit and Musical Fidelity all make similarly priced, high quality DACs that are worth considering. It is strictly a matter of personal preference.