Preheat the oven to 400 degrees F. Line a large baking sheet with parchment paper; set aside.
Roll out each puff pastry sheet to a 12 by 14-inch rectangle. Place on the baking sheet and fold over the edges of each pastry to form a 1/2-inch border. Prick the bottom of pastry with a fork; set aside.
Arrange tomatoes, artichoke hearts, and cheeses on puff pastry. Sprinkle with Italian seasoning.
Bake in preheated oven for 20 to 25 minutes or until edges are puffed and golden brown.