Thaw shrimp if frozen. In a Dutch oven bring black-eyed peas and the water to boiling; reduce heat. Simmer, covered, 45 minutes or until tender; drain.
Meanwhile, peel and devein shrimp, leaving tails intact if desired. Rinse shrimp; pat dry. In a large skillet heat oil over medium heat. Add white onion, celery, and sweet pepper; cook 5 to 7 minutes or until vegetables are tender, stirring occasionally. Add chicken and sausage; cook and stir 5 to 6 minutes or until starting to brown. Stir in tomato paste; cook 2 minutes more. Stir in tomatoes, broth, Cajun seasoning, and cooked black-eyed peas. Bring just to boiling. Stir in shrimp. Simmer 2 to 3 minutes or until shrimp are opaque.
Serve jambalaya over rice. Sprinkle with green onions and, if desired, parsley. If desired, pass hot pepper sauce.