HEAT oven to 350°F.
COOK spaghetti in large saucepan as directed on package, omitting salt and adding spinach to the boiling water for the last minute.
MEANWHILE, cook and stir onions in butter in large skillet 5 min. Stir in mushrooms; cook and stir 4 min. or until mushrooms release their liquid. Add flour; cook and stir 1 min. Add broth; cook and stir 4 min. or until thickened.
DRAIN spaghetti mixture; return to pan. Add mushroom mixture, chicken, cooking creme and 3 Tbsp. Parmesan; mix well. Pour into 13x9-inch baking dish sprayed with cooking spray; cover.
BAKE 25 min. Top with mozzarella and remaining Parmesan; bake, uncovered, 8 to 10 min. or until spaghetti mixture is hot and bubbly and mozzarella is melted.