This article addresses the simultaneous actuator and sensor fault estimation (FE) problem for a class of Markovian jump systems (MJSs) with nondifferentiable actuator failures. In order to overcome the difficulties brought by the nondifferentiable actuator failures, we construct an extended vector composed of states, sensor faults, and disturbances, where the derivatives of actuator failures are not required in this augmented system. Then, two novel observer-based approaches are developed for the augmented descriptor system to cope with the FE problem. The first one is a reduced-order FE observer, where the actuator failures can be estimated by the algebraic input reconstruction strategy. The second one refers to an iterative learning observer (ILO) design method, which can obtain the accurate FE result by integrating the estimations in the iterative processes. The two proposed FE observer design methods can avoid the sliding surface switching problem produced by sliding-mode observers in the area of MJSs. Finally, a practical example of the F-404 aircraft engine system is presented to show the validity of the proposed FE observer design techniques.