Identifying modules from biological networks is important since modules reveal essential mechanisms and dynamic processes in biological systems. Existing algorithms focus on identifying either active modules or topological modules (communities), which represent dynamic and topological units in the network, respectively. However, high-level biological phenomena, e.g., functions are emergent properties from the interplay between network topology and dynamics. Therefore, to fully explain the mechanisms underlying the high-level biological phenomena, it is important to identify the overlaps between communities and active modules, which indicate the topological units with significant changes of dynamics. However, despite the importance, there are no existing methods to do so. In this paper, we propose MUMI (MUltitask Module Identification) algorithm to detect the overlaps between active modules and communities simultaneously. Experimental results show that our method provides new insights into biological mechanisms by combining information from active modules and communities. By formulating the problem as a multitasking learning problem which searches for these two types of modules simultaneously, the algorithm can exploit their latent complementarities to obtain bettersearch performance in terms of accuracy and convergence. Our MATLAB implementation of MUMI is available at https://github.com/WeiqiChen/Mumi-multitask-module-identification.