Preheat oven to 400 degrees F (200 degrees C). Prepare a glass baking dish by spraying with nonstick cooking spray.
Mix together yogurt, mayonnaise, lemon juice, tarragon, dill, mozzarella, and Parmesan in a small bowl. Place fish fillets into prepared baking dish, and spread evenly with cheese mixture.
Bake in preheated oven until fish flakes when tested with a fork, about 15 minutes.