In this paper, the finite horizon mixed H2/H∞ control problem is studied for the systems governed by Ito-type nonlinear stochastic differential equations with state, control and external disturbance-dependent noise. It is shown that the mixed H2/H∞ control under consideration is associated with the four cross-coupled Hamilton-Jacobi equations in nonlinear case. Some necessary and/or sufficient conditions for the existence of finite horizon stochastic H2/H∞ controllers are derived. In particular, some previous results on deterministic and stochastic H∞ (H2/H∞) can be viewed as simple corollaries of our main theorems