Future network environments will be heterogeneous and mobile terminals will have the opportunity to dynamically select among many different access technologies. Therefore, it is important to provide service continuity in case of vertical handoffs when terminals change the access technology. Two important wireless access technologies are WLAN (Wireless Local Access Networks) and WMAN (Wireless Metropolitan Access Networks) networks. In this paper, we address several challenges related to a seamless integration of those technologies. We highlight important aspects for designing a WLAN/WMAN interworking architecture and we address important Quality of Service (QoS) issues for such interworked systems like degree of QoS support provided by the technologies, QoS mapping and signalling for vertical handoff. By formulating several interworking scenarios, where WLAN users with ongoing voice, video and data sessions hand over to WMAN, we study QoS and performance issues and analyse feasibility of seamless session continuity through simulations.