As a new kind of optimization problems, multiobjective multifactorial optimization(MO-MFO) problems have attracted much attention in recent years. Its main feature is that only a single population can be used to optimize multiple multiobjective optimization tasks simultaneously. In this paper, a multifactorial evolutionary algorithm based on decomposition(MFEA/D) strategy is proposed. It decomposes a MO-MFO problem into a series of single objective optimization subproblems through multiple sets of weight vectors, and optimizes them simultaneously with a single population. In the process of population evolution, the information communication strategy between different tasks with a certain probability is proposed to mine useful information between different tasks, so as to accelerate the convergence rate of each task. The statistical analysis of the experiment results on 10 benchmark MO-MFO problems illustrates that the information communication strategy can help to accelerate the convergence rate and that the proposed MFEA/D strategy performs significantly better than the state-of-the-art MO-MFEAs in the literature.