Whisk the cream cheese in a large bowl with an electric mixer on medium speed until creamy. Gradually add the coffee and milk, whisking until well blended. Place a spoon in a serving bowl or 10 dessert glasses, refrigerate for several hours or until ready to serve. Top with the rest of the whipped topping just before serving.
When initially served, cappuccino consists only of espresso and froth, but liquid milk quickly settles into the foam to form the (approximately) equal parts of foam, steamed milk and espresso, for which cappuccino is known. Once you acquire two basic barista skills (making drinks and making froth with milk), you can learn how to make a cappuccino yourself.