This paper deals with the problem of passivity and passification for stochastic Markovian jump systems with incomplete transition rates and actuator saturation. By use of the polytopic model, sufficient conditions are built such that the closed-loop constrained system is stochastically passive. The procedure of deriving a state feedback controller is converted into an optimization problem with a set of linear matrix inequalities. Finally, the simulation results of a linearized dynamic model of a vertical take-off and landing aircraft in the vertical plane illustrate the effectiveness of the proposed schemes.