In this paper, we consider optimization problems where the objective is the sum of a function given by an expectation and a Lipschitz continuous convex function. For such problems, we pro- pose a Stochastic Composite Proximal Bundle (SCPB) method with optimal complexity. The method does not require estimation of parameters involved in the assumptions on the objective functions. Moreover, to the best of our knowledge, this is the first proximal bundle method for stochastic programming able to deal with continuous distributions. Finally, we present the results of numerical experiments where SCPB slightly outperforms Stochastic Mirror Descent.