Preheat oven to 400 degrees.
In a large pot boil about 8 cups of water. Add the 1st five ingredients and cook for 20-25 minutes or until chicken is cooked and tender
Complete this step while the chicken is cooking. In a blender, mix the cream cheese and chicken broth until smooth and creamy. Set aside.
In a skillet over medium heat, melt the butter and oil. Add the onion and jalapeno. Season with salt and pepper and cook for about five minutes. Add the garlic and cook for about 1 more minute.
Stir in the can of chilies and the cream cheese sauce. Mix together just until heated up and set aside.
Get the chicken out of the pot and shred it up and allow to cool slightly.
Add to a large bowl, season with 1 tbs of chicken bouillon and pepper and add 1 cup each of the grated cheeses. Mix together well.
If you are using corn tortillas, wrap them in some damp paper towels and microwave them for about 1 minute. OR you can fry them in some oil for about 10 seconds per side. This step is important because they will fall apart while you are assembling them if you skip it. If you are using flour tortillas, there is no need for this step.
Layer about 1.5 cups of the cream cheese sauce in an 11x13 baking dish. Lay a tortilla in the sauce, fill with a spoonful of the chicken mixture and roll it up. Repeat this process until you have used all of the chicken mixture.
Pour the rest of the cream cheese sauce on top and spread out evenly. Top with the remaining cheeses. Bake for about 20 minutes, until cheese is golden brown and bubbly. Let cool for about 10 minutes before serving.