In this paper, dynamic resource management is investigated for serving on-demand video streaming users in heterogeneous wireless networks (HWNs) with time varying channel conditions. The HWN is equipped with multi-homing capability, simultaneously connecting to different wireless interfaces. In order to take advantage of the time varying nature of wireless channels, we utilize the joint quality selection associated with quality adjustment at application layer and resource allocation associated with power allocation, subcarrier assignment, and time fraction determination at physical layer to perform the dynamic resource management. By using Lyapunov optimization technique, we develop a quality-aware streaming (QAS) algorithm to maximize the network utility, which is the difference of time-averaged users' perceived video quality and time-averaged HWN's transmit power. Simulation results exhibit that the proposed QAS algorithm can significantly improve network utility compared with the state-of-art baselines, which are not specific for on-demand video streaming.