This paper studies the infinite horizon mixed H-2/H-infinity control for discrete-time stochastic systems with state and disturbance dependent noise. We shall first establish a version of stochastic bounded real lemma (SBRL) which by itself has theoretical importance. Based on the SBRL, it is shown that under the condition of exact observability, the existence of a static state feedback H-2/H-infinity controller is equivalent to the solvability of four coupled matrix-valued equations. A suboptimal H-2/H-infinity controller design is given based on a convex optimization approach and an iterative algorithm is proposed to solve the four coupled matrix-valued equations. (c) 2008 Elsevier Ltd. All rights reserved.