Heat the olive oil in a Dutch oven or large pot over medium heat. Stir in the sausage, and cook for 2 minutes. Add the chicken, onion, bell pepper, and celery; season with salt and Cajun seasoning. Cook and stir until the vegetables are soft, 6 to 8 minutes. Stir in the sauteed rice until evenly coated in the vegetable mixture, then pour in the tomatoes with juice, garlic, chicken broth, bay leaves, and thyme leaves. Bring to a simmer over medium-high heat, then reduce heat to medium-low, cover, and simmer 20 minutes.
After 20 minutes, stir in the shrimp, and cook 10 minutes uncovered until the shrimp turn pink and are no longer translucent in the center. Remove the pot from the heat, and let stand 5 minutes. Discard the bay leaves before serving.