Roboticists have begun to design biologically inspired robots with soft or partially soft bodies, which have the potential to be more robust and adaptable, and safer for human interaction, than traditional rigid robots. However, key challenges in the design and manufacture of soft robots include the complex fabrication processes and the interfacing of soft and rigid components. We used multimaterial three-dimensional (3D) printing to manufacture a combustion-powered robot whose body transitions from a rigid core to a soft exterior. This stiffness gradient, spanning three orders of magnitude in modulus, enables reliable interfacing between rigid driving components (controller, battery, etc.) and the primarily soft body, and also enhances performance. Powered by the combustion of butane and oxygen, this robot is able to perform untethered jumping.