How To Separate Unwanted Sound From My Vocals?

[Gigfree]

Good afternoon, all! 

I recently recorded vocals for a small film using a Zoom H5 and a Senheisser MKE600.

While recording, I heard music while monitoring the audio with headphones, but not when I removed my headphones.

Is there a way to separate and remove this music from my audio without damaging the vocals I need?

What could have caused my recorder to catch the music but without me actually hearing it without the recorder? 

I've included a take where you can hear the music right from the beginning. 

[SteveG_AudioMasters_]

I can't hear music, but I can hear a loud, variable hum, and that's almost certainly some form of interference. Whatever it is, it's not quite 60Hz but close. Audition's notch filter will probably all but eliminate it, but you will have to be careful with the harmonics, of which there are a lot.