The use of interactive media has already gained considerable popularity. Interactivity gives viewers VCR controls like slow-motion, pause, fast-forward, and instant replay. However, traditional server-based or client-based approaches for supporting interactivity either consume too much network bandwidth or require large client buffering; and hence they are economically unattractive. In this paper, we propose the architecture and design of an interactive media proxy (IMP) server that transforms noninteractive broadcast or multicast streams into interactive ones for servicing a large number of end users. For IMP to work cost-effectively, it must carefully manage its storage devices, which are needed for caching voluminous media data. In this regard, we propose a fine-grained device management strategy consisting of three complementary components: disk profiler, data placement, and IO scheduler. Through quantitative analysis and experiments, we show that these fine-grained strategies considerably improve device throughput under various workload scenarios.