The wireless network that integrates a heterogeneous cellular network and a WLAN is referred to as a WLAN/cellular integrated network (WCIN). In a fourth generation WCIN, in order to achieve collision-avoidance between the LTE-A and IEEE 802.11 family, some interference-free mechanisms, such as carrier sense adaptive transmission and listenbefore- talk, are proposed. However, the interference-free medium access mechanisms leave some unexploited partially overlapped 802.11ac channels, which result in a waste of spectrum. In this paper, we propose an interference-tolerant medium access method to optimize the WCIN throughput by utilizing those partially overlapped channels (POCs). First, we show the feasibility of enhancing WLAN throughput by utilizing 802.11ac POCs in a WCIN. Second, we mathematically model the partial overlap when an 802.11ac channel is partially overlapping with an LTEA component carrier. Third, we propose an interference-tolerant medium access mechanism to optimize the WCIN throughput. The interference-tolerant one ensures that the interference to LTE-A users is tolerable in a given WCIN. Finally, we construct a hardware-in-the-loop testbed to evaluate and compare our proposed mechanism with three other state-of-the-art mechanisms. The experimental results show that our approach achieves at most 39% more throughput than one of the state-of-the-art collisionavoidance mechanisms regarding the entire WCIN.