In a large Dutch oven, heat oil over medium high heat; add sausage and chicken, and cook about 5 minutes or until browned. Add onion, celery, and bell pepper, and cook, stirring frequently, about 3 minutes or until tender. Add garlic, stirring for about 30 seconds until fragrant. Add rice, and stir about 3 minutes until lightly toasted.
Add tomatoes, and stir until juices are absorbed. Add broth, thyme, and bay leaves. Bring to a boil; reduce heat to medium-low. Cover, and cook for 15 minutes or until rice is tender.
In a medium bowl, combine shrimp, 1 teaspoon salt, 1/2 teaspoon black pepper, paprika, cayenne, and parsley. Add shrimp to rice mixture, and stir until combined. Cook for 2 minutes or until shrimp are pink and firm. Add remaining 1 teaspoon salt and 1/2 teaspoon black pepper.
Garnish with green onion, if desired. Serve immediately.