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Content Distribution is a key application in an infrastructure-based wireless network. Existing works on this area use either pure broadcast transmission or pure unicast transmission. In this paper, we propose a hybrid broadcast-unicast transmission scheme to improve the efficiency of content distribution for wireless networks with multi-rate support. In the proposed scheme, access point broadcast packets to nodes within its transmission range with a deliberately selected broadcast rate. After that, the point-to-point unicast transmissions are exploited for data forwarding. It mitigates the inherit problems that comes from unicast and broadcast transmission respectively, such as severe contention and large amount of redundant re-transmission. Furthermore, cooperative communication is exploited as a physical layer technique to enhance the throughput of the network. A cooperative communication aware routing is designed accordingly, where the contention relationship between wireless links have been taken into consideration. Simulation results show that the proposed scheme outperforms existing schemes dramatically in terms of network throughput and transmission delay.