Heat the olive oil in a large, enameled pot over medium heat. Add the onion, bell pepper, and celery and cook for 6 to 7 minutes, or until soft. Add the mushrooms and garlic, stir, and cook until the mushrooms are soft. Add the remaining ingredients, except the seafood and parsley, and bring to a simmer. Simmer for 10 to 15 minutes, uncovered, tasting to adjust the seasonings.
About 15 to 20 minutes before serving, add the seafood. Stir to mix and thoroughly coat. Cover and simmer for 10 to 12 minutes, or until the fish flakes easily and the shellfish have opened. Discard any mussels or clams that have not opened. Remove the bay leaf. Serve in large soup bowls and garnish individual portions with parsley.