This paper is concerned with the fault and state estimation problem for Markovian jump systems (MJSs) with simultaneous actuator and sensor faults. To deal with the design issues, we propose a novel descriptor reduced-order sliding mode observer (SMO), based on which the estimation of the actuator faults, sensor faults, and the states can be obtained simultaneously. Compared with the traditional SMO design issues in MJSs, we reconstruct the actuator faults directly without employing the equivalent output error injection method. Thus, the reachability analysis of the sliding surface is not necessary. The superiority of this kind of the SMO method is that the sliding surface switching problem is avoided. Finally, the effectiveness (as suggested by the theoretical results) of the approach described is tested on a mobile manipulator by simulation studies.