In a large Dutch oven, melt butter over medium-high heat; cook onion, celery and garlic until softened. Add green and red pepper, bay leaves, oregano, thyme, salt, pepper and cayenne. Cook until all softened and remove from pot.
Add sausage to the pot and start to brown; add chicken. When they are starting to brown well, add vegetables back to the pot.
Add rice and stir well. Add tomatoes, tomato sauce and stock; bring to boil. Stir in shrimp.
Bake, covered in a 375 degree oven for 40 minutes or until rice is tender. Discard bay leaves.
Sprinkle individual servings with parsley and green onions.