The increasing demand of online high-quality video streaming has brought huge challenges to the traditional client- server video streaming systems due to high feedback delay, rigorous bandwidth requirement, and the lack of a mechanism of centralized resource management between users. In this work, we propose AMIS-MU, an edge computing-based mobile video streaming system that optimizes the watching experience of users via playback adaptation and channel resource allocation. Thanks to the plenty of computation capacity at the edge server, all the decision-making and computation-intensive tasks are conducted at the edge without imposing any burden on mobile users. Video playback speed manipulation, bitrate adaptation, and dynamic channel allocation empower AMIS-MU to optimize the quality of experience (QoE) from both the application and the physical layer. To solve this cross-layer joint optimization problem, we creatively leverage the state value function obtained from the deep reinforcement learning (DRL) as a bridge between these two layers which significantly reduces the problem complexity. And we resort to Lyapunov optimization to solve the non-convex sub-channel and transmit power allocation problem to provide users with rational and fair network services. Experiments show that AMIS-MU outperforms other existing algorithms in terms of average QoE and fairness.