Melt butter in a large skillet over medium heat; cook and stir bell pepper and onion until vegetables are tender, about 5 minutes. Remove from heat and stir in chicken, shrimp, cream of shrimp soup, French onion soup, diced tomatoes, andouille sausage, chicken broth, and rice. Transfer mixture to a baking dish.
Bake in preheated oven until rice is tender, about 1 1/2 hours.
