I just drilled straight into them.

Let me try to draw an ASCII diagram:

---|__|
---|__|
--//__\\___

so that is what is coming from the chrome piece. The top part fits into holes in the black piece. You want to drill that top part away until you have this left:

---____
--//__\\___

(disregard the dashed lines on the left, they are just spacers)

once you are left with those little tabs, you are going to drill holes in them so you can screw everything back together.