This paper studies the effect of passive and active impedance for protecting jumping robots from landing impacts. The theory of force transmissibility is used for selecting the passive impedance of the system to minimize the shock propagation. The active impedance is regulated online by a joint-level controller. On top of this controller, a reflex-based leg retraction scheme is implemented which is optimized using direct policy search reinforcement learning based on particle filtering. Experiments are conducted both in simulation and on a real-world hopping leg. We show that although the impact dynamics is fast, the addition of passive impedance provides enough time for the active impedance controller to react to the impact and protect the robot from damage.