Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish.
In a large skillet, brown the sausage over medium heat. Remove the sausage and set aside, leaving the drippings in the pan.
Add the chicken pieces to the skillet and cook until browned on all sides. Remove the chicken and set aside with the sausage.
In the same skillet, add the chopped onion, bell pepper, celery, and garlic. Sauté until the vegetables are softened, about 5 minutes.
Stir in the diced tomatoes (with juices), rice, chicken broth, water, Cajun seasoning, smoked paprika, thyme, cayenne pepper, black pepper, and bay leaf. Bring the mixture to a simmer.
Stir in the browned sausage and chicken. Transfer the mixture to the prepared baking dish.
Cover the dish with aluminum foil and bake for 30 minutes. Remove the foil, stir in the shrimp, and bake uncovered for an additional 10-15 minutes, or until the shrimp are cooked through and the rice is tender.
Remove the bay leaf and stir in the chopped parsley before serving.