The increasing adoption of the internet of things (IoT) has led to the need for systems with higher spectral and energy efficiency (SE and EE) in order to enable communication. Larger data rate demands had led researchers to look at millimeter wave (mmWave) bands to boost network rates. This paper investigates the downlink performance of a three-tier heterogeneous network (HetNet) that consists of sub-6 GHz macrocells overlaid with small cells operating on both the mmWave and sub-6 GHz bands. A model is developed using tools from stochastic geometry to analyze the coverage, rate, ASE and EE of such a network. Various deployment strategies and their impacts on the considered metrics are studied. Simulation results are used to verify the validity of the proposed model.