Preheat oven to 325°F (163°C). Grease a 9×13 inch pan.
Combine the crust ingredients in a small bowl. Press the mixture into the bottom of the prepared pan.
Bake the crust for 10 minutes, then set aside to cool.
To make the blackberry filling, combine the sugar, cornstarch and water in a medium-sized saucepan over medium heat and stir to combine. Heat until the mixture is wet and the sugar begins to melt.
Add the mashed blackberries and stir into the sugar mixture.
Continue cooking and stirring until the mixture is thickened, about 5-7 minutes.
Remove from heat, then pour the mixture into another bowl and refrigerate until cool. You should have about a 1/2 cup (89g) of the blackberry filling.
To make the mousse layers, add the cream cheese and sugar to a large mixer bowl and beat until well combined and smooth.
Add the milk and mix until well combined. Set aside.
In another large mixer bowl, add the heavy whipping cream, powdered sugar and vanilla extract. Whip on high speed until stiff peaks form.
Carefully fold about 1/3 of the whipped cream into the cream cheese mixture, then add the remaining whipped cream and fold until well combined.
Set aside about 3 cups of the mousse. Add about half of the lime juice and the lime zest to the remaining mousse and gently fold to combine.
Add the remaining lime juice and fold until well combined.
Pour the lime mousse on top of the crust and spread into an even layer. Place in the refrigerator while you work on the blackberry layer.
Add the cooled blackberry filling to the 3 cups of mousse you set aside earlier. Gently fold until well combined.
Drop spoonfuls of the blackberry layer over the top of the lime layer and then spread into an even layer.
To finish of the lush, add the heavy whipped cream, powdered sugar and vanilla extract for the whipped cream topping to a large mixer bowl. Whip on high speed until stiff peaks form.
Spread the whipped cream into an even layer on top of the blackberry layer and then top with blackberries and lime slices.
Refrigerate until ready to serve. Dessert is best for 3-4 days.