The heterogeneous cellular networks (HCNs) with device-to-device (D2D) communications have been a promising solution to cost-efficient delivery of high data rates. A key challenge in such D2D-enabled HCNs is how to design an effective association scheme with D2D model selection for load balancing. Moreover, the offloaded users and D2D receivers (RXs) would suffer strong interference from BSs, especially from high-power BSs. Evidently, a good association scheme should integrate with interference mitigation. Thus, we first propose an effective resource partitioning strategy that can mitigate the interference received by offloaded users from high-power BSs and the one received by D2D RXs from BSs. Based on this, we then design a user association scheme for load balancing, which jointly considers user association and D2D model selection to maximize network-wide utility. Considering that the formulated problem is in a nonlinear and mixted-integer form and hard to tackle, we adopt a dual decomposition method to develop an efficient distributed algorithm. Simulation results show that the proposed scheme provides a load balancing gain and a resource partitioning gain.