To my understanding (and per the original manual), both the drivers and passenger door locks should operate in the following fashion:

If the door is locked from inside and you step out of the car and close the door, the lock will pop up (to prevent you from locking your keys in the car). This can be bypassed by pressing/holding the button on the external door handle while you close the door, or you simply can lock the door with the key.

This is how my passenger door currently operates.

On...

1967 Mustang Door Latch Proper Operation?