With the emergence of Mobile Crowdsensing Systems (MCSs), many auction schemes have been proposed to incentivize mobile users to participate in sensing activities. However, in most of the existing work, the heterogeneity of MCSs has not been fully exploited. To tackle this issue, in this paper, we study the joint problem of sensing task assignment and scheduling while considering partial fulfillment, attribute diversity, and price diversity. We first elaborately model the problem as a reverse auction and design a distributed auction framework. Then, based on this framework, we propose two distributed auction schemes, costpreferred auction scheme (CPAS) and time schedule-preferred auction scheme (TPAS), which differ on the methods of task scheduling, winner determination, and payment computation. We further rigorously prove that both CPAS and TPAS can achieve computational-efficiency, individual-rationality, budgetbalance, and truthfulness. Finally, the simulation results validate the effectiveness of both CPAS and TPAS in terms of sensing tasks allocation efficiency, mobile users working time utilization and utility, and truthfulness.