Next-generation wireless networks must enable emerging technologies such as augmented reality and connected autonomous vehicles via wide range of wireless services that span enhanced mobile broadband (eMBB), as well as ultra-reliable low-latency communication (URLLC). Existing wireless systems that solely rely on the scarce sub-6 GHz, microwave ($μ$W) frequency bands will be unable to meet such stringent and mixed service requirements for future wireless services due to spectrum scarcity. Meanwhile, operating at high-frequency millimeter wave (mmWave) bands is seen as an attractive solution, primarily due to the bandwidth availability and possibility of large-scale multi-antenna communication. However, mmWave communication is inherently unreliable due to its susceptibility to blockage, high path loss, and channel uncertainty. Hence, to provide URLLC and high-speed wireless access, it is desirable to seamlessly integrate the reliability of $μ$W networks with the high capacity of mmWave networks. To this end, in this paper, the first comprehensive tutorial for \emph{integrated mmWave-$μ$W} communications is introduced. This envisioned integrated design will enable wireless networks to achieve URLLC along with eMBB by leveraging the best of two worlds: reliable, long-range communications at the $μ$W bands and directional high-speed communications at the mmWave frequencies. To achieve this goal, key solution concepts are discussed that include new architectures for the radio interface, URLLC-aware frame structure and resource allocation methods along with mobility management, to realize the potential of integrated mmWave-$μ$W communications. The opportunities and challenges of each proposed scheme are discussed and key results are presented to show the merits of the developed integrated mmWave-$μ$W framework.