The unlicensed spectrum is recently considered one of the defining solutions to meet the steadily growing traffic demand. This, in turn, has led to the enhancement for LTE in Release-13 to enable Licensed-Assisted Access (LAA) operations. The design of the medium access control (MAC) protocol for the LAA system to harmonically coexist with the incumbent WLAN system operating in an unlicensed band is critical and challenging. In this paper, we consider an Integrated Access and Backhaul (IAB) system coexisting with a Wi-Fi network operating at millimeter-wave (mmWave) unlicensed spectrum, for which a listen-before-talk-based (LBT) based medium access mechanism is carefully designed. Additionally, we have considered an in-band system that supports both access and backhaul in a single node where the small-cell or the IAB nodes compete with the WiGig for medium access. We present comprehensive experimental results and give design insights based on the simulation results.