Whisk together first 4 ingredients.
Melt 1 teaspoon butter in a small nonstick skillet coated with cooking spray over medium-high heat, rotating pan to coat bottom evenly.
Add half of egg mixture to skillet. As egg mixture starts to cook, gently lift edges of omelet with a spatula, and tilt pan so uncooked portion flows underneath. Cook 3 minutes or until almost set. Flip omelet over.
Sprinkle 1 side of omelet with half each of ham and cheeses. Fold in half. Cook 1 to 2 minutes or until cheese melts. To make next omelet, repeat with remaining 1 teaspoon butter, egg mixture, ham, and cheeses. Serve immediately.