I have this image and I want to make it transparent even where the white rectangles are.
But in illustrator this is not as easy as it may seem.
They're normal rectangles, but I can't do it...
Can you please tell us what this is? A vector graphic? Or a placed raster image?
Please do show what's in the layers panel.
Then select all and make a compound path? Does that not work?
If those are normal vector shapes, you sould be able to select them and the black rectangle and go to Object > Compound Path > Make
Or if they decide to make a nuissance of themselves when you make the Compound Path as suggested by Doug, you can (also) use Pathfidner>Minus front to make the Compound Path.
And if all of the above doesn't work.
Use the Shape Builder tool (Shift-M) and drag over the white areas with the Alt key pressed.