In this note, we consider the finite horizon mixed H-2/H-infinity control problem for discrete-time stochastic linear systems subject to Markov jump parameters and multiplicative noise. Firstly, we derive a stochastic bounded real lemma (SBRL), which is used to establish a necessary and sufficient condition for the existence of the mixed H-2/H-infinity control via the solvability of four coupled difference matrix-valued recursions (CDMRs). Moreover, a state feedback H-2/H-infinity controller is designed by means of the solutions of CDMRs.