Preheat the oven to 350 degrees F.
In a Dutch oven, add the russet potatoes and enough of the water to just cover them.
Grease two 7x11-inch or 9x13-inch baking dishes.
In a large saucepan, add the sweet potatoes and enough of the water to just cover them.
Place the Dutch oven and the saucepan on the stovetop and bring them both to a boil.
Reduce the heat to medium-low for both and cover them.
Cook until the russet potatoes and the sweet potatoes are both tender, about 10-15 minutes.
Drain the sweet potatoes.
Add 1 carton of the cream cheese, 1/2 cup of the sour cream, and 1/4 cup of the Colby Jack cheese to the sweet potatoes and mash to combine.
Drain the russet potatoes.
Add the remaining cream cheese and the remaining sour cream to the russet potatoes and mash to combine.
Add the milk, 1/4 cup of the parmesan cheese, the salt, and the black pepper to the russet potatoes and stir gently to combine.
Add 1 1/3 cups of the russet potato mixture to each of the prepared baking dishes, spreading it out evenly in each dish.
Layer 1/2 of the sweet potato mixture into each prepared baking dish, spreading it out evenly.
Repeat the layers using 1 1/3 cups of the remaining russet potato mixture and the remaining sweet potato mixture.
Top the layers in each baking dish with an even amount of the remaining russet potato mixture.
Bake both casseroles, uncovered, until heated through, about 15 minutes.
In a bowl, add the remaining Colby Jack cheese and the remaining parmesan cheese.
Sprinkle the topping mixture evenly over both of the casseroles.
Bake until the cheese on top is melted, about 2-3 minutes.
Garnish with the green onions and serve hot.