Bring a large pot of lightly salted water to a boil; add penne and cook, stirring occasionally, until tender yet firm to the bite, about 11 minutes. Drain. Transfer to large serving bowl.
Place green and red bell peppers, tomato, mushrooms, olives, and pepperoni in the bowl of pasta.
Whisk mayonnaise, Italian dressing, garlic, oregano, salt, and pepper together in a bowl. Pour over pasta mixture and toss to coat evenly. Top with mozzarella cheese and grated Parmesan cheese. Refrigerate at least 1 hour to chill before serving.