Preheat oven to 375°F / 190°C and grease a 9×13 inch baking dish.
Add 1½ cups uncooked long grain rice to the baking dish.
In a bowl, whisk together 2 cups chicken broth, 1 cup milk, and 1 can cream of mushroom soup until smooth.
Stir in 2 cups cooked chicken, 2 cups sliced mushrooms, ½ cup chopped onion, 2 minced garlic cloves, 1 teaspoon salt, ½ teaspoon black pepper, and ½ teaspoon dried thyme.
Pour the mixture over the rice and stir lightly to combine. Spread everything evenly in the baking dish.
Cover tightly with foil and bake for 40 minutes.
Remove the foil, stir the rice, then sprinkle 1 cup shredded mozzarella cheese and ½ cup grated Parmesan cheese over the top.
Return the dish to the oven uncovered and bake for another 10 minutes until the cheese is melted and the rice is tender.
Remove from oven and let the casserole rest for 5 minutes, then sprinkle with 2 tablespoons chopped parsley before serving.