The newspaper can withstand 35 damage before being destroyed.
Strategies
With
The newspaper has a decent amount of health, making the zombie somewhat protected. However, due to its head and back being vulnerable, it does not have a very large effect. Because of this, use Newspaper Zombies as you would with Browncoat Zombies i.e. as a distraction and to help capture the garden.
Against
Focus on the back and head, as the newspaper has more health than the zombie itself. If you are playing as a Chomper, chomping it from behind or below will be a waste of time, as you can just destroy the paper by biting it. However, if you eat the newspaper, you will earn 25 coins, which is greater than the amount you would earn if you destroyed the newspaper by biting it and vanquished the zombie. If you want extra coins, eat the paper. If you want to quickly get rid of the zombie, bite the paper.
Gallery
Plants vs. Zombies Wiki has a gallery for Newspaper Zombie.
It may appear that it still attempts to attack plants with the newspaper, even when it is destroyed.
If it stands still for enough time (and he has its newspaper), it will play an animation where the newspaper starts blowing away in the air, and the Newspaper Zombie jumps and grabs it.
Its newspaper protects it from Chomper's attack when it is about to swallow this zombie. This trait happens with all shielded zombies.
Instead of attacking nearby plants, it rushes to the Player's Garden after losing his newspaper.
It sounds different from the other zombies and mostly sounds like an old man.
It makes an appearance in the "Grumps" and "Toilet Troubles" special waves.
Even with the newspaper, when vanquished by this zombie the attack still reads "Zombie Hurt."
This applies to the Map Pirate and Screen Door Zombie.
In Plants vs. Zombies: Garden Warfare 2, the player can faintly hear the "Grr!" sound of the original Newspaper Zombie from Plants vs. Zombies when its newspaper is destroyed.
In Garden Warfare 2, there is a relatively common glitch where Newspaper Zombie's newspaper is invisible, but still present.