Preheat oven to 350 degrees F (175 degrees C). Grease a 10-inch tube pan.
Whisk flour, baking powder, and baking soda together in a bowl.
Beat butter and sugar together in a bowl until creamy. Add marzipan. Add eggs one at a time, beating well after each addition. Beat half-and-half into butter mixture.
Stir 1 cup of flour mixture into the butter mixture. Stir in milk. Add another 1 cup flour mixture to the butter mixture and stir milk into mixture. Add remaining flour mixture and stir in orange juice. Scrape down the sides of the bowl with a spatula and give batter a final mix. Pour batter into prepared tube pan.
Bake in the preheated oven until a toothpick inserted in the center of the cake comes out clean, about 90 minutes.
Cool cake in the pan for 15 to 20 minutes before turning out onto a wire rack to cool completely.