This paper introduces the concept of hybrid operational space control, a method that unifies kinematic tracking of individual joints with an inverse dynamics task space controller for the remainder of the robot. The proposed control strategy allows for a hierarchical task decomposition while simultaneously regulating the inner forces between the contact points. At the same time it improves fast tracking for compliant systems by means of appropriate low level position controllers. Introducing StarlETH, a compliant quadrupedal robot, the applicability of the controller and the hardware is demonstrated in realtime simulations and hardware experiments. We perform static walking in challenging terrain and show how the controller can combine precise and fast position control with robust and compliant interaction with the environment.