Preheat oven to 375°F (190°C).

In a saucepan, combine 2 cans of cream of chicken soup with 1 can of water.

Add chopped green chilies to the soup mixture and heat through.

In a skillet, brown ground beef and onion over medium heat.

Drain any excess grease from the browned beef and onion mixture.

Add the refried beans and chili beans to the skillet with the beef and onion.

Mix the bean and meat mixture thoroughly.

Spread a small amount of the meat mixture on each flour tortilla.

Roll up the tortillas to form burritos.

Arrange a layer of burritos in a greased long cake pan.

Pour half of the cream of chicken soup mixture evenly over the first layer of burritos.

Create a second layer of burritos on top of the first.

Pour the remaining cream of chicken soup mixture over the second layer of burritos.

Top the entire casserole with shredded Cheddar cheese and Co-Jack cheese.

Bake in the preheated oven until the cheese is melted and bubbly, approximately 50 minutes.