Heat olive oil in a large pot or Dutch oven over medium-high heat.
Add sausage and chicken, cook until browned. Remove and set aside.
In the same pot, sauté onion, bell pepper, celery, and garlic until softened.
Stir in the diced tomatoes, rice, broth, seasonings, and return sausage and chicken to the pot.
Bring to a boil, then reduce heat, cover, and simmer for about 20 minutes.
Add shrimp, cover again, and cook an additional 5-7 minutes, until shrimp is pink and cooked through.
Garnish with fresh parsley before serving, if desired.