Preheat the oven to 350°F (175°C) and lightly grease a 9x13-inch baking dish.
In a large bowl, stir together the cream of chicken soup, cream cheese, cottage cheese, and milk until smooth and creamy.
Fold in the shredded chicken, cheddar cheese, mozzarella cheese, Italian seasoning, salt, and black pepper until well combined.
Spread the mixture evenly into the prepared baking dish and smooth the top.
In a small bowl, mix the crushed Ritz crackers, melted butter, and Parmesan cheese until evenly coated.
Sprinkle the cracker topping evenly over the casserole and bake uncovered for 30–35 minutes, until bubbly and golden brown.