Heat olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat.
Add sliced smoked sausage and cook for 3-4 minutes until browned. Remove sausage and set aside.
Add chicken pieces to the pot and cook for 5-6 minutes until browned on all sides. Remove and set aside with the sausage.
Reduce heat to medium and add diced onion, green bell pepper, and celery to the pot. Cook for 5 minutes until vegetables are softened.
Add minced garlic and cook for 1 minute until fragrant.
Return sausage and chicken to the pot. Stir in diced tomatoes with their juice, rice, penne pasta, chicken broth, smoked paprika, oregano, thyme, cayenne pepper, black pepper, and salt. Stir well to combine.
Bring the mixture to a boil, then reduce heat to low. Cover the pot and simmer for 15 minutes, stirring occasionally to prevent sticking.
After 15 minutes, add the raw shrimp on top of the pasta mixture. Cover and cook for an additional 5-7 minutes until shrimp are pink and cooked through and the pasta is tender.
Remove the pot from heat and let it sit covered for 5 minutes.
Fluff the jambalaya with a fork and garnish with sliced green onions and chopped parsley before serving.