sausage and chicken ...jambalaya?

I'm not sure what to call this. There's no roux, so it might not be exactly a gumbo. It's relatively simple and Baby D can be distracted long enough for me to chop up the ingrediants and then it's a matter of throwing them in the pot.

1pkg Cajun style sausage (I find them at Target)
1 or 2 Chicken breast
1 Tbsp olive oil
1 Onion
2 carrots
1 Green Pepper
1 4oz can diced green chilis
1 14oz cans diced tomatoes
1/2 cup water
1/3 cup white rice
1/2 tsp Ground cumin
1 tsp Cajun seasoning
1/2 tsp chili powder
1/2 tsp Old bay (optional)
1/2 tsp cayenne powder (optional)

Chop onion carrots and green pepper. Heat oil in pot, add vegetables. Stir over medium heat until softened. Add chilis. Stir for another minute. Add chopped sausage and chicken. stir until cooked through. Add spices. Simmer and stir for 2 or 3 minutes. Add tomatoes and water. Add rice. Bring to boil. Cover and simmer over low heat for 15 minutes.