In the bowl of an electric mixer fitted with the paddle attachment, beat the butter, shortening, and vanilla at medium speed until blended, about 2 minutes. Scrape down the sides of the bowl with a rubber spatula, then beat on high speed until light and fluffy, about 2 minutes.
Add the cream cheese and mix at medium- low speed just until combined (overmixing the frosting at this point will make it grainy).
Gradually add the confectioners’ sugar and mix at medium- low speed until well blended and creamy, about 2 minutes. Cover the bowl and refrigerate the frosting for at least 2 hours before using.