Add both cans of chili to a 4-5 quart saucepan over medium heat, stirring constantly.
Stir in the chunky salsa and continue stirring often until the chili and salsa are completely combined and heated through. About 5-8 minutes.
Keep the stovetop heat on medium, and add in the softened cubed cream cheese. Keep stirring constantly until the cream cheese has melted into the chili. (You can mash the cubes of cream cheese while stirring to help the incorporation process)
Stir in the 2 cups freshly shredded cheddar cheese, stirring constantly until the cheddar cheese has melted.
Stir in the shredded pepper jack cheese. Remove from the heat. Top with the remaining ½ cup of cheddar cheese and sprinkle with the chopped cilantro.
Serve immediately with corn chips.
Cover and chill in the refrigerator for up to 2 days.