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Proxy caching is a key technique to reduce transmission cost for on-demand multimedia streaming. The effectiveness of current caching schemes, however, is limited by the insufficient storage space and weak cooperations among proxies and their clients, particularly considering the high bandwidth demands from media objects. In this paper, we propose COPACC, a cooperative proxy-and-client caching system that addresses the above deficiencies. This innovative approach combines the advantages of both proxy caching and peer-to-peer client communications. It leverages the client-side caching to amplify the aggregated cache space and rely on dedicated proxies to effectively coordinate the communications. We propose a comprehensive suite of distributed protocols to facilitate the interactions among different network entities in COPACC. It also realizes a smart and cost-effective cache indexing, searching, and verifying scheme. Furthermore, we develop an efficient cache allocation algorithm for distributing video segments among the proxies and clients. The algorithm not only minimizes the aggregated transmission cost of the whole system, but also accommodates heterogeneous computation and storage constraints of proxies and clients. We have extensively evaluated the performance of COPACC under various network and end-system configurations. The results demonstrate that it achieves remarkably lower transmission cost as compared to pure proxy-based caching with limited storage space. On the other hand, it is much more robust than a pure peer-to-peer communication system in the presence of node failures. Meanwhile, its computation and control overheads are both kept in low levels.