Brown the Meats:

In a large, deep skillet or Dutch oven, cook the Andouille sausage over medium heat until it's nicely browned. Remove it with a slotted spoon and set aside.
In the same pot, add the chicken pieces seasoned with a bit of salt and pepper. Cook until browned on all sides. Remove and set aside with the sausage.

Sauté the Vegetables:

In the remaining fat, sauté the onion, bell pepper, and celery until softened, about 5 minutes. Add the garlic and cook for another minute until fragrant.

Combine Ingredients:

Return the sausage and chicken to the pot. Stir in the rice, diced tomatoes, chicken stock, Creole seasoning, paprika, thyme, oregano, and bay leaves. Season with salt and pepper to taste.

Cook the Jambalaya:

Bring the mixture to a boil, then reduce the heat to low. Cover and simmer for about 20-25 minutes, or until the rice is nearly cooked.

Add the Shrimp:

Stir in the shrimp and cook for another 5-10 minutes, or until the shrimp are pink and the rice is tender.

Garnish and Serve:

Remove the bay leaves. Adjust seasoning if necessary. Garnish with chopped parsley and sliced green onions before serving.