Why do you wanna turn off the music anyway?!
Can't you just go in the options and lower the music sound?!
Sadly, no. Call of duty only allows you one master sound slider. That includes Foley, dialog and music.
Seriously, when I am doing a stealth mission in special ops, the last thing I want to hear is some stupid song blasting into my ears, I need to hear the foot steps of the enemy so I can get a rough Idea of where they are with out having to look directly at them while running the risk of getting spotted.
Music on the battlefield while in a firefight... like I got a whole orchestra ticked away in my ammo pouches.