Heat oven to 375 degrees. Cook pasta in large saucepan as directed on pkg, adding broccoli for the last 3 min.
Meanwhile, heat large nonstick skillet on medium-high heat. Add Chicken; cook 3 min. or until no longer pink, stirring frequently. Stir in broth; simmer 3 min or until chicken is done. Add Neufchatel cheese; cook and stir on low heat 1 min or until melted. Stir in 1/2 cup mozzarella.
Drain pasta and broccoli. Add to chicken mixture; mix lightly. Spoon into 8" square baking dish; cover.
Bake 15 min. or until heated through. Sprinkle with remaining cheeses. Bake uncovered 3 min or until melted. Let stand 5 min.