Preheat your oven to 350°F (175°C). Grease and flour three 8-inch round cake pans, then line each with parchment paper.
In a medium-sized bowl, whisk together the flour, baking powder, and salt. Set aside.
In a stand mixer fitted with the paddle attachment, beat the softened butter and orange zest until creamy. Add the sugar and mix on medium-high speed until the mixture is light and fluffy, about 3 minutes.
Reduce the speed to low, adding the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
With the mixer on low speed, alternate adding the dry flour mixture with the milk and orange juice, starting and ending with the dry ingredients. Add the flour mixture in three parts and the milk and orange juice in two parts, mixing until just combined after each addition.
Gently fold the floured cranberries into the batter until evenly distributed.
Divide the batter evenly among the prepared cake pans, smoothing the tops.
Bake for 25-30 minutes or until a toothpick inserted into the center of the cakes comes out mostly clean. Allow the cakes to cool in the pans on a wire rack for 10 minutes before turning them out onto the rack to cool completely.