Melt butter in a large saucepan over medium-high heat. Add ham and cook 2 minutes.
Add sausage and chicken. Brown for about 5 minutes, stirring frequently and scraping the pan bottom. Add seasoning mixture.
Stir in onion, celery, green pepper, and garlic. Cook for 5 minutes. Add stock, tomatoes, and puree. Reduce heat and simmer for about 45 minutes, stirring occasionally.
Remove bay leaves. Allow jambalaya to stand 5 minutes before serving. Serve with rice.