Cook the pasta in a large pot of salted boiling water, per the package instructions. Before draining, reserve 1/2 cup of the pasta water and set aside. Drain and set aside.
Preheat the oven to 350°F and lightly spray a 9x13-inch baking dish with nonstick cooking spray.
Season the chicken with the salt and pepper.
Heat the oil in a large skillet over medium-high heat. Add the chicken and cook until it is no longer pink, allowing some to brown a bit. It doesn't need to be cooked completely through. Use a slotted spoon to remove the chicken to a bowl. Cover and set aside.
Add a small amount of additional oil if necessary, then add the onions and peppers to the skillet. Cook over medium heat until soft - about 5 minutes. Add the garlic and cook for 1 minute. Return the chicken to the pan and mix well. Set aside.
In the large pot that you cooked the pasta in, add the alfredo sauce, cream cheese, and the reserved pasta water. Heat over medium-low heat, stirring frequently, until the cream cheese has melted and the sauce is smooth. Add the pasta, chicken, and vegetables to the pot and mix well to combine. Pour the mixture into the prepared baking dish and sprinkle wtih the Italian blend cheese. Bake in the preheated oven for about 20 minutes or until the cheese is melted and bubbly.