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This paper is concerned with the stabilization problem for a class of Markovian stochastic jump systems against sensor fault, actuator fault and input disturbances simultaneously. In the proposed approach, the original plant is first augmented into a new descriptor system, where the state vector, disturbance vector and fault vector are assembled into the state vector of the new system. Then, a novel augmented sliding mode observer is presented for the augmented system and is utilized to eliminate the effects of sensor faults and disturbances. An observer-based mode-dependent control scheme is developed to stabilize the resulting overall closed-loop jump system. A practical example is given to illustrate the effectiveness of the proposed design methodology.