In a small skillet (or small saucepan) over medium heat, heat olive oil. Add garlic, stirring often, and cook until fragrant, about 1 minute.
Add cream cheese, breaking up the cream cheese with a wooden spoon, and cook until melted. Whisk in milk and cook until mixture is heated through.
Add feta, mozzarella, yogurt, lemon juice, dill, parsley, lemon zest, and red pepper flakes. Season with salt and pepper and cook until the cheeses have melted, about 5 minutes.
Remove from heat, then drizzle with olive oil. Garnish with more dill and parsley. Sprinkle with kalamata olives and tomatoes.
Serve warm with pita chips for dipping.