There are two different methods that can be used here. Use whichever you're more comfortable with.
Method 1: Pathfinder
The reason the pathfinder likely wasn't working for you is because pathfinder doesn't take strokes into account. Here's what I would do in your specific scenario:
- Remove the strokes from the black objects.
- Select the top black object, and choose Object -> Path -> Offset Path.
- Enter the negative version of half your old stroke width*. For example, enter -0.5pt if your stroke was 1pt. This will create a new path that is slightly smaller.
- Delete the old path. Now you should see part of the white object showing through.
- Now select the new top black object and the white object, and use Pathfinder -> Minus front. You should end up with one white object with the black background showing through.
You'll most likely have to repeat this process for each of the 3 letters individually, as pathfinder wouldn't correctly handle all three at once.
*Note: This is assuming you have it as the default of aligning stroke to center.
Method 2: Live Paint Group
This method may be more intuitive for some people, and may be easier for your specific case.
- Select all the non-background objects.
- Choose Object -> Live Paint -> Make.
- Choose Object -> Live Paint -> Expand.
- Use the Direction Selection tool to select and delete the parts you want to be transparent.