I think this is what is happening, and what you are asking.
You've deleted the back box already.
The yellow would represent the white, the navy would be the black.
You need to break the object apart, and combine the proper paths.
Make two objects out of one.
You will likely have to work in wireframe after you 'break apart' the graphic.
So, break apart, and combine, are the two commands you're after.
* the second is actually one 'compound path' over a 'path' I believe,
if you wanna get technical, but whatever.