This paper proposes a joint design of the routing strategy over the fronthaul network and the transmission strategy over the wireless network in a downlink cloud radio access network (C-RAN), in which the remote radio heads (RRHs) are connected to the central processor (CP) via multi-hop routers. The data-sharing strategy is adopted, where the CP multicasts each user's data to all the RRHs serving this user via the multihop fronthaul network, which then cooperatively serve the users through joint beamforming. Such a setting naturally provides an opportunity for applying the technique of network coding to efficiently reduce the multicast traffic in the fronthaul network. A novel cross-layer optimization framework is then investigated, where the RRH's beamforming vectors as well as the user- RRH association in the physical-layer, and the network coding design in the network-layer are jointly optimized to maximize the throughput of C- RAN subject to fronthaul link capacity constraints. This paper proposes a two-stage algorithm to solve this problem using the techniques of sparse optimization and successive convex approximation. Simulation results are provided to verify the effectiveness of the proposed cross-layer design in the downlink multi- hop C-RAN.