Hybrid turbine airfoil components containing a ceramic material, in which detailed features of the components are formed of materials other than ceramic materials. The components include a first component formed of a ceramic-based material and a second component formed of a metallic material. The first component comprises an airfoil portion and a nub, and the second component is separately formed and attached to the first component by casting the metallic material around the nub of the first component. The second component includes a platform portion between the airfoil portion and the nub of the first component and a dovetail portion on the nub of the first component. Each of the platform and dovetail portions has at least one off-axis geometric feature that results in the second component having a more complex geometry than the first component.