Season the sausage and chicken pieces with half of the cajun seasoning.
Heat 1 tablespoon of oil in a heavy-bottomed pot over medium-high heat. Cook the sausage until it becomes lightly browned.
Add another tablespoon of oil into the same pan, add the chicken pieces, and cook until lightly browned on all sides. Transfer everything to a plate and set aside.
Add the remaining oil, bell peppers, celery, jalapeño, and onion. Cook for 5 to 6 minutes, stirring occasionally until the onions are softened. Add the garlic and cook until fragrant—about 1 minute.
Stir in crushed tomatoes, cajun seasoning, thyme, cayenne, bay leaf, red pepper, salt, and pepper. Leave to simmer for 5 minutes, stirring occasionally.
Stir in the chicken and sausage. Add the rice, chicken, sausage, and Chicken broth and bring to a rapid boil. Turn the heat down to low and continue to cook for 20 to 25 minutes. (Read notes).
Place the Shrimps over the jambalaya, stir gently but quickly, cover again with the foil and lid, and leave to cook for another 5 to 6 minutes until the shrimps become pink and cooked through.
Adjust the seasoning if necessary. Discard the bay leaf.Remove from heat and enjoy!.