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In conventional Wireless Mesh Networks (WMNs), multihop relays are performed in the backbone comprising of interconnected Mesh Routers (MRs) and this causes capacity degradation. This paper proposes a hybrid WMN architecture that the backbone is able to utilize random connections to Access Points (APs) of Wireless Local Area Network (WLAN). In such a proposed hierarchal architecture, capacity enhancement can be achieved by letting the traffic take advantage of the wired connections through APs. Theoretical analysis has been conducted for the asymptotic capacity of three-tier hybrid WMN, where per-MR capacity in the backbone is first derived and per-MC capacity is then obtained. Besides related to the number of MR cells as a conventional WMN, the analytical results reveal that the asymptotic capacity of a hybrid WMN is also strongly affected by the number of cells having AP connections, the ratio of access link bandwidth to backbone link bandwidth, etc. Appropriate configuration of the network can drastically improve the network capacity in our proposed network architecture. It also shows that the traffic balance among the MRs with AP access is very important to have a tighter asymptotic capacity bound. The results and conclusions justify the perspective of having such a hybrid WMN utilizing widely deployed WLANs.