Cook pasta in large saucepan as directed on package, omitting salt and adding spinach to the boiling water for the last minute.
Meanwhile, cook and stir chicken and basil in large nonstick skillet sprayed with cooking spray on medium-high heat 3 min. Stir in tomatoes and pasta sauce; bring to boil. Simmer on medium-low heat 3 min. or until chicken is done, stirring occasionally. Add Neufchatel; cook and stir 1 to 2 min. or until completely melted.
Drain pasta mixture; return to pan. Stir in chicken mixture and 1/2 cup mozzarella; spoon into 2-qt. casserole sprayed with cooking spray.
Bake 20 min. or until heated through; top with remaining cheeses. Bake 3 min. or until mozzarella is melted.