Technically, neither the Challenger nor the Charger are on a frame.
Being "unicoupe" or unibody, the strength in the car comes from the rocker panels and the floorpan.
So, the question is: do the Charger and Challenger share the same stampings? Yes, and no!
The Challenger is based on the Charger floorpan, but shortened by several inches, which is the difference in the wheelbase. The trunkpan is unique to the Challenger. The framerails are the same between the two cars, and everything from the firewall forward is exactly the same in all of the LX cars, including the Magnum and the 300.
In addition, all of the suspension components can be swapped across the board on all the LX cars.