Remove casings from sausage. Combine sausage and chicken in a large saucepan coated with cooking spray over high heat; cook 2 minutes, stirring to crumble sausage. Add onion and thyme; cook 2 minutes, stirring occasionally. Add celery, carrot, and broth; bring to a boil.
Remove rice from bag; stir into broth mixture. Cover, reduce heat to medium, and cook 7 minutes or until rice is tender. Discard thyme sprigs. Stir in parsley, salt, and pepper.