Melt the milk chocolate chips in 20-second microwave bursts, stirring between each, until smooth. Let cool 1 minute.
In a large bowl, whisk the heavy cream, milk, sugar, cocoa powder, vanilla, and salt until the sugar dissolves. Whisk in the melted milk chocolate until no streaks remain.
Pour into a Ninja Creami pint below the max fill line. Lid and freeze level for 24 hours.
For the mousse, melt the white chocolate chips the same way and cool slightly. Beat the cream cheese, powdered sugar, and vanilla until smooth, then beat in the white chocolate. Whip the ½ cup heavy cream to soft peaks and fold it in. Refrigerate.
Lock the frozen pint into the Creami and run the Ice Cream function. Re-spin once if crumbly.
Make a well down the center, add about half the mousse, and run Mix-In (or fold by hand in 3–4 strokes for a bolder swirl).
Scoop and serve, topping with the remaining mousse.