Traditional cellular networks require the downlink (DL) and uplink (UL) of mobile users (MUs) to be associated with a single base station (BS). However, the power gap between BSs and MUs in different transmission environments results in the BS with the strongest downlink differing from the BS with the strongest uplink. In addition, the significant increase in the number of wireless machine type communication (MTC) devices accessing cellular networks has created a DL/UL traffic imbalance with higher traffic volume on the uplink. In this paper, a joint user association and resource partition framework for downlink-uplink decoupling (DUDe) is developed for a tiered heterogeneous cellular network (HCN). Different from the traditional association rules such as maximal received power and range extension, a coalition game based scheme is proposed for the optimal user association with DUDe. The stability and convergence of this scheme are proven and shown to converge to a Nash equilibrium at a geometric rate. Moreover, the DL and UL optimal bandwidth partition for BSs is derived based on user association considering fairness. Extensive simulation results demonstrate the effectiveness of the proposed scheme, which enhances the sum rate compared with other user association strategies.