Mobile crowdsensing (MCS) is a new paradigm to collect sensing data and infer useful knowledge over a vast area for numerous monitoring applications. In urban environments, as more and more applications need to utilize multi-source sensing information, it is almost indispensable to develop a generic mechanism supporting multiple concurrent MCS task assignment. However, most existing multi-task assignment methods focus on homogeneous tasks. Due to the diverse spatiotemporal task requirements and sensing contexts, MCS tasks often differ from each other in many aspects (e.g., spatial coverage, temporal interval). To this end, in the paper, we present and formalize an important Heterogeneous Multi-Task Assignment (HMTA) problem in mobile crowdsensing systems, and try to maximize data quality and minimize total incentive budget. By leveraging the implicit spatiotemporal correlations among heterogeneous tasks, we propose a two-stage HMTA problem-solving approach to effectively handle multiple concurrent tasks in a shared resource pool. Finally, in order to improve the assignment search efficiency, a decomposition-and-combination framework is devised to accommodate large-scale problem scenario. We evaluate our approach extensively using two large-scale real-world data sets. The experimental results validate the effectiveness and efficiency of our proposed approach