We characterize a two tier heterogeneous network, consisting of classical sub-6 GHz macro cells, and multi radio access technology (RAT) small cells able to operate in sub-6 GHz and millimeter-wave (mm-wave) bands. For optimizing coverage and to balance loads, we propose a two-step mechanism based on two biases for tuning the tier and RAT selection, where the sub-6 GHz band is used to speed-up the initial access procedure in the mm-wave RAT. First, we investigate the effect of the biases in terms of signal-to-interference-plus-noise ratio (SINR) distribution, cell load, and user throughput. More specifically, we obtain the optimal biases that maximize either the SINR coverage or the user downlink throughput. Then, we characterize the cell load using the mean cell approach and derive upper bounds on the overloading probabilities. Finally, for a given traffic density, we provide the small cell density required to satisfy system constraints in terms of overloading and outage probabilities. Our analysis highlights the importance of deploying dual-band small cells, in particular, when small cells are sparsely deployed or in case of heavy traffic.