Complex sentence: The 3rd Parachute Battalion would land on their own DZ north of the bridge, and secure the high ground there, while the 2nd Parachute Battalion did the same in the south.
Split into simpler sentences: The 3rd Parachute Battalion would land on their own DZ north of the bridge, and secure the high ground there. While the 2nd Parachute Battalion did the same in the south.