In a large bowl, use an electric mixer to beat the butter and cream cheese at medium speed until creamy. Gradually add the powdered sugar 1/2 cup at a time, beating at low speed until blended.
Increase speed to medium, and slowly add milk and vanilla, beating until smooth.
Microwave the chocolate chips in a microwave-safe bowl at MEDIUM 1 1/2 to 2 minutes or until melted and smooth, stirring at 30 second intervals. Gradually add melted chocolate to mixture; beat until blended and smooth.
If the frosting is too soft for spreading, cover and refrigerate for a few minutes until it firms up a little bit.
When cakes are cool, place one cake on cake stand. Place a generous cup of frosting in the middle and spread evenly, using an off set icing spatula or rubber spatula or knife.
Place second cake on top of frosted cake.
Place remaining frosting on top and spread out toward the edges, the frosting will start to leak over the edges. Use your off set icing spatula or rubber spatula or knife to spread around the edges, spreading smoothly.