How would you separate the background in this photo?

The black looks pretty black to me. Just paint in any areas that aren't perfect with a brush.

Here's how I would make the bg blacker Mike. I would dup. the original and separate the kids from the bg using a mask. On the original layer, I would use a levels adj. layer and use the 'set black point' eyedropper to darken the blacks. Above the masked layer, I would add a second levels adj. layer clipped to the masked layer to adjust the tones of the kids. I'd also try to do a better job of masking on the original, full rez. image.

I practiced everyone's advice and things came out great. I used layers, masking, etc. to really isolate the subjects and wipe out the background (without making look like they were cut out with a pair of scissors).

Overall it was a good experience for my first time shooting against a black background. Next time I'll get it right in camera and with lighting before dealing with software.

This is one of my favorites. The main part of the job was shooting their daughter in her dance outfit.