When the brakes are pressed hard why would the car make a thumping sound?

More details would help a lot but going on the details you provided. I would guess possibly a defective strut or strut mount. A defective spring or one of its components. A defective shock and or possibly a bad ball joint. I would try pushing up and down on each corner of the car and see if you hear the sound then try to pin point where the sound is coming from and go from there. If you still don't know see a pro. , EzForJesus

This may be too simple of an answer so i apologise if it is too simple but your 96 Intrepid is equipped with anti-lock brakes. When your brakes lock up by pressing the pedale reall hard the car automatically will pump them at a super fast pace helping to slow the car better. Your car also might come with "Traction Control" Basically what this does is if the wheels are spinning it again will use the anti lock feature to try to regain traction so you may feel the same thumping on ice or real wet roads.