This paper investigates a heterogeneous cellular network (HCN) topology, where multiple sub-6 GHz bands are available for access and device-to-device (D2D) links with the full-duplex (FD) mode, and an integrated millimeter-wave (mm-wave) band is added to the D2D links' sub-channel resource options. D2D links share spectrum resources of cellular users or dedicated mm-wave sub-channel. Densely deployed small cells scenario provides an ideal platform to implement mm-wave, FD and D2D communications. With large bandwidths available, mm-wave has the potential to meet the expected extreme data rate demands. Leveraging highly directional beamforming, severe transmission loss and the blockage phenomenon of mm-wave can be alleviated. Theoretically, FD communications can double the spectral efficiency due to bi-directional communications with the same spectral and temporal resources. However, such benefit comes at the cost of residual self-interference (RSI). Multi-user interference (MUI) and RSI among network uplink, downlink and D2D links are the main challenges. In the paper, we formulate an optimization problem for FD access and D2D links sub-channel allocation underlaying HCNs combining sub-6 GHz and mm-wave bands to make the system transmission rate maximized. Then, a scheme based on the coalition formation game is proposed to deal with this challenging NP-complete optimization. Finally, performance evaluation investigates the suitable conditions for FD and HD operations. Under different network parameter settings, we quantify associated performance of proposed scheme.