Preheat the oven to 375°F (190°C).
Bring a large pot of water to a boil and cook the penne pasta according to package directions, omitting added salt; add the spinach to the boiling water during the last minute of cooking to wilt.
Meanwhile, spray a large nonstick skillet with cooking spray and heat over medium-high; add the chicken and dried basil and cook, stirring, for about 3 minutes until starting to brown and nearly cooked through.
Stir in the spaghetti sauce, minced garlic, and drained diced tomatoes, bring to a boil, then reduce heat and simmer 3 minutes or until the chicken is cooked through.
Stir the cubed Neufchâtel cheese into the chicken mixture until incorporated and smooth.
Drain the pasta and spinach mixture in a colander and return to the pot; add the chicken and sauce mixture and 1/2 cup of the shredded mozzarella and stir to combine.
Spoon the combined mixture into a 2-qt casserole dish or 8-inch square baking dish and bake for 20 minutes.
Remove from the oven, sprinkle with the remaining mozzarella and the Parmesan, and return to the oven for about 3 minutes more, until the mozzarella is melted.