In a large Dutch oven, heat 2 tablespoons of the olive oil over medium high heat.
Season shrimp with Creole seasoning and sauté until almost cooked through, about 4 minutes. Using a slotted spoon, remove shrimp and set aside until later, much later.
Season chicken pieces with Creole seasoning. Add remaining olive oil to Dutch oven and when hot, add chicken pieces and sauté until browned on both sides, about 8 minutes. Remove and set aside.
Add sausage and cook until browned.
Add onion, celery, bell pepper, garlic, bay leaves, cayenne and thyme and cook until vegetables are wilted, about 5 minutes.
Add tomatoes, chicken stock, and water and return chicken pieces to pot. Season with salt and pepper and simmer, covered, for 15 minutes.
Remove chicken, pull from bones and break into smaller pieces, return meat to pot. Continue to simmer 30 minutes.
If serving immediately, cook rice according to directions, reserve for serving Jambalaya over. Otherwise, stop here. Cool and refrigerate Shrimp and Jambalaya mix to be used another day.
Add green onions and parsley to Dutch oven, and continue to simmer, covered, for another 10 minutes.
Add Shrimp. Remove from heat and let sit 10 minutes before serving over rice.