Multi-rate multicasting has become more and more attractive in contemporary multimedia applications because of its efficiency in serving heterogeneous receivers with different rates commensurate with their capabilities. When network coding is applied to multi-rate media multicasting to achieve additional gain, we encounter several significant challenges in designing a scheme that attains maximum throughput for all heterogeneous users. In this paper we focus on the problem of designing optimal network coding based approach to maximize total received utility for multi-rate multicasting media encoded in a layered structure. Such a layered structure facilitates multi-rate media delivery that matches users' reception capabilities but creates certain undesired dependency between different layers. We propose a request-assign mechanism to enable sufficient information propagation between source node and receiver node before multicasting the media content. With the help of request messages, the proposed scheme can overcome challenges of the layered dependency and is able to determine maximal decodable layer for each individual receiver. Furthermore, the proposed scheme achieves maximal decodable rate with polynomial complexity. Experiment results on JPEG-2000 images verify the proposed scheme.