In current multi-channel live P2P video systems, there are several fundamental performance problems including exceedingly-large channel switching delays, long playback lags, and poor performance for less popular channels. These performance problems primarily stem from two intrinsic characteristics of multi-channel P2P video systems: channel churn and channel-resource imbalance. In this paper, we propose a radically different cross-channel P2P streaming framework, called View-Upload Decoupling (VUD). VUD strictly decouples peer downloading from uploading, bringing stability to multichannel systems and enabling cross-channel resource sharing. We propose a set of peer assignment and bandwidth allocation algorithms to properly provision bandwidth among channels, and introduce substream swarming to reduce the bandwidth overhead. We evaluate the performance of VUD via extensive simulations as well with a PlanetLab implementation. Our simulation and PlanetLab results show that VUD is resilient to channel churn, and achieves lower switching delay and better streaming quality. In particular, the streaming quality of small channels is greatly improved.