In a large pot, heat the vegetable oil over medium heat. Add the chicken and beef, browning them on all sides for about 5-7 minutes.
Add the chopped onion and minced garlic to the pot, cooking until the onion is translucent, about 3-4 minutes.
Pour in the chicken broth, beef broth, and water. Stir in the carrots, potatoes, green beans, corn, diced tomatoes, thyme, oregano, salt, pepper, and bay leaf.
Bring the mixture to a boil, then reduce the heat to low. Cover and simmer for 1 to 1.5 hours, stirring occasionally, until the meat is tender and the vegetables are cooked through.
Remove the bay leaf before serving. Adjust seasoning with more salt and pepper if desired. Serve hot.