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, melt butter in large skillet on medium heat. Add onions; cook and stir 5 min. Stir in mushrooms; cook and stir 4 min. or until mushroom liquid is cooked off. Add flour; cook and stir 1 min. Stir in broth; cook 4 min. or until thickened, stirring constantly.
MIX cream cheese spread, milk and seasonings until blended. Drain spaghetti mixture; return to pan. Add cream cheese mixture, mushroom mixture, chicken and 3 Tbsp. Parmesan; mix well. Spoon 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.