The increasing demand for the coverage of high-speed wireless local area networks (WLANs) is driving the installation of a very large number of access points. Wireless mesh networks (WMNs) have emerged as a promising technology in next generation networks to provide economical and scalable broadband access to wireless interconnection of multiple access points which manage individual WLANs in order to extend the coverage of conventional single WLANs. Due to various types of applications with particular purposes running at different WLANs, the traffic generated by stations in different WLANs possess a high degree of heterogeneity. To the best of our knowledge, there is hardly any analytical model reported in the current literature to handle heterogeneous network traffic in the integrated WMNs and WLANs. To fill this gap, we develop a new analytical model to investigate the Quality-of-Service (QoS) performance metrics in WMNs interconnecting multiple WLANs with heterogeneous stations. The Poisson process is employed to model the traffic of non-bursty data applications and the Markov modulated Poisson process (MMPP) is used to model the traffic of bursty multimedia applications. Extensive simulation experiments are conducted to validate the accuracy of the analytical model.