Emerging fifth generation (5G) wireless networks require massive bandwidth in higher frequency bands, extreme network densities, and flexibility of supporting multiple wireless technologies in order to provide higher data rates and seamless coverage. It is expected that utilization of the large bandwidth in the millimeter-wave (mmWave) band and deployment of heterogeneous networks (HetNets) will help address the data rate requirements of 5G networks. However, high pathloss and shadowing in the mmWave frequency band, strong interference in the HetNets due to massive network densification, and coor- dination of various air interfaces are challenges that must be addressed. In this paper, we consider a relay-based multiband orthogonal frequency division multiple access (OFDMA) HetNet in which mmWave small cells are deployed within the service area of macro cells. Specifically, we attempt to exploit the distinct propagation characteristics of mmWave bands (i.e., 60 GHz- the V-band - and 70-80 GHz -the E-band-) and the Long Term Evolution (LTE) band to maximize overall data rate of the network via efficient resource allocation. The problem is solved using a modified dual decomposition approach and then a low complexity greedy solution based on iterative activity selection algorithm is presented. Simulation results show that the proposed approach outperforms conventional schemes.