Preheat oven to 350°. In a large skillet, heat butter over medium-high heat. Add peppers and onion; cook and stir until peppers are tender, 4-6 minutes., Stir in flour and seasonings until blended; gradually stir in milk. Bring to a boil, stirring constantly; cook and stir until thickened, about 1 minute. Stir in cream cheese until blended. Add pepper jack, chicken and green chiles; heat through, stirring to combine. Transfer to a greased 11x7-in. baking dish., Prepare cornbread batter according to package directions. Spread over chicken mixture. Bake, uncovered, until golden brown and a toothpick inserted in topping comes out clean, 35-40 minutes. Let stand 10 minutes before serving.