Heat pot over medium-high heat.
Cook sausage until browned, about 5 minutes.
Add chicken pieces to the pot.
Cook chicken until golden, 8 minutes.
Remove meats, set aside.
Add onions, peppers, celery to pot.
Sauté vegetables until soft, 5 minutes.
Stir in garlic, cook 1 minute.
Add rice, stir constantly 2 minutes.
Pour in chicken broth slowly.
Add paprika, cayenne, thyme, bay leaves.
Return meats to pot, stir gently.
Bring mixture to a boil.
Reduce heat, cover, simmer 20 minutes.
Add shrimp in final 5 minutes.
Remove from heat, let stand 5 minutes.
Garnish with green onions before serving.