The paper deals with robust filtering algorithms for discrete systems with unknown inputs (disturbances) and Markovian jump parameter. The proposed filtering algorithm is based on the separation principle, minimization of a quadratic criterion and the use of Kalman filters with unknown input and smoothing procedures. Solving a non-stationary problem is represented solving a two-point boundary value problem in kind of difference matrix equations. In the stationary case problem is represented matrix algebraic equations. Robustness ensures the stability of the filter dynamics when errors occur in identifying the jump parameter. An example is provided to illustrate the proposed approach, which showed that the use of smoothing procedures for estimating an unknown input improves the accuracy of estimates.