Noise cancellation for known sources
If you have audio that will be played by TV beforehand, then this problem becomes almost similar to echo cancellation, i.e. adaptive filters could be used and cancellation will be great.

What we have is the audio that will be played through TV, this audio will be used as reference for adaptive filter and input to the adaptive filter would be the capture(noisy music in earphone/headphone).
so adaptive filter will try to estimate the TV's audio in the earphone capture, then this estimate could be subtracted from earphone capture to get noise free(TV noise) music in earphone/headphone.