Heat the butter and olive oil in a large Dutch oven or soup pot over medium heat. Add the onion, then season with salt and pepper. Sauté until the onion is tender.
Add the diced tomatoes, crushed tomatoes, seafood stock, chicken stock, dried oregano, dried thyme, and bay leaf. Increase the heat to bring the mixture to a simmer.
Increase the heat to medium-high and add the mixed seafood and chopped parsley to the pot. Cook for 2-4 minutes, or until the seafood is just cooked through.