Without seeing it, it's hard for me to visualize what you're talking about. Here's three scenarios I am getting from your description.
1. You have a solid filled layer with white and a black border on it. You applied the bevel and it worked because it's an edge effect. You applied a drop shadow and it didn't work because there are actual white pixels on the same layer and it's adding the shadow where there
aren't pixels.
2. You have the black border
below the white (or whatever it is) fill. The bevel worked because the black border is exposed, but the shadow is showing up
under the other artwork.
3. You have toggled some bizzare combination of buttons you didn't mean to in your "advanced blending options" window of your layer effects, and have inadvertantly changed how the knockout is working. You can have layer styles clipped by transparency, layer masks, and vector masks. You can also have them knockout other layers as well as blend their effects in different orders. Any one of these might cause unexpected results if you hadn't built the file to take them into account and weren't prepared for them.
In any case, the best solution would be to make the 20px black border it's own layer on the top of the layer stack and then apply your layer effects to it.
If that doesn't help, all I can say is show us the problem because we're not getting it from a description.