In theory if you have the original recording you can simply subtract it from the recording.
The only time I've tried doing this the original recording was on 1/4" tape and despite having lots of money on offer to make it work I failed, badly. If everything is in the digital domain and the music was mixed digitally into the dialog you might get lucky. If it was a field recording and it was just music playing in the background I'd say you don't have a chance at getting rid of it.
Works best only when the vocals are on a separate track. Otherwise, all the commercial software that do this kill the dynamic range of the music and most of the time you can still hear the vocals.
If the background music is quieter than the voice by some way, you could try using an expander plug in. This should at least reduce the background music and increase the voice. Experiment with settings, never tried it for video work, but could help. Better than a gate i think as you are spacing out the highs and the lows further.
But this is tricky one, doubt you can remove it fully. Bobs subtraction sounds good too.
Sound Forge Audio Studio contains a Voice Eraser which can be reversed for Vocal Only. http://www.sonycreativesoftware.com/audiostudio/effects May-or-may-not work for you. Might be worth downloading the trial and give it a shot.
A recording engineer friend of mine uses the old saying that goes something like "you can remove music from vocals or vocals from music about as easy as you can take the eggs out of a cake after you bake it".
Of course, all vocal erasers start off with the idea that the vocal is mono, panned dead center. A camcorder recording of a voice is most likely going to be stereo with a lot of difference between the channels, making it just as mutable as the music.