Preheat oven to 350 degrees F. Prepare three 9" round cake pans by greasing with oil and a paper towel, flouring, and placing a parchment paper round at the bottom of each.
Beat the butter, shortening, and sugar with an electric mixer until white and fluffy, about 4 min. Then add the eggs one at a time, making sure to NOT over beat. (Scrape down the sides after with a spatula.)
In a separate bowl, sift together flour, baking powder, and salt. In a measuring cup, whisk the whole milk, buttermilk, and vanilla extract together. Add this liquid mixture alternately with the flour mixture into the butter mixture, beginning and ending with dry ingredients. GENTLY stir all ingredients until combined, being sure to scrape down sides and bottom of bowl to make sure everything is incorporated.
Distribute the batter evenly between the three pans and bake for 25 min, or until a toothpick inserted in the middle of the cakes comes out clean. Remove from oven and let cake cool for 5 min in pans, then release cakes onto a wire rack to cool completely.
Pour the whipping cream into a small bowl and using a handheld electric mixer, mix until it becomes the consistency of fluffy whipped cream. (Takes between 1-2 minutes mixing on high speed.)
In a medium bowl, mix with an electric mixer on medium speed the cream cheese, powdered sugar, lemon extract, lemon zest, and lemon juice together until combined. Scrape the sides of the bowl, then using a spatula gently fold the whipped cream into the cream cheese mixture. Set aside in the fridge until ready to use.
In a large bowl, beat the butter using an electric mixer on medium speed until it turns white and fluffy. Scrape down the sides after.
Add in the rest of the ingredients mixing on low first and then increasing the speed to high for about 2-3 minutes. If frosting is too thin, add in another cup of powdered sugar, if it's too thin add in a Tbsp at a time of cream.
Place the first cake layer onto a cake board on a revolving cake stand. Cut about an 1" off the end of a piping bag, fill it with the buttercream frosting and pipe a rim of frosting around the edge of the cake. Fill the centre of the cake layer spoonful by spoonful of the lemon cream filling, being sure not to fill it so high that it goes over the buttercream rim. (If you fill it too high, the cake will lose its stability.)
Place the second cake layer on top and repeat the last steps. (You'll most likely have left over lemon cream filling, feel free to add dollops to the cake plates later as it tastes delicious with the berries!)
Place the third cake layer on top, get eye-level with the cake to make sure you're putting on the cake layers evenly. Fill your piping bag with the lemon buttercream and pipe it all around the sides and top of the cake. Using an offset spatula, smooth the top of the cake. Using a cake scraper, scrape around the cake whilst spinning the cake stand to smooth out the sides.
Decorate with an assortment of fresh berries!