Explosive growth of bandwidth-intensive multime-dia applications may impose a heavy traffic burden on wirelesslinks of heterogeneous networks (HetNets), which also requiressubstantial energy consumption. Edge caching is emerging toreduce the service latency and relieve the huge burden on thebackhaul links in HetNets. Moreover, millimeter wave (mmWave)spectrum with huge available bandwidth has been regarded asa promising technology to satisfy the high capacity demands infuture HetNets. However, the high directionality coupled withharsh propagation environment makes mmWave communicationvulnerable to blockage, which makes link establishment andmaintenance challenging. In this paper, we propose a jointmaximum distance separable (MDS) coded caching and trans-mission problem for a mmWave HetNet, aiming at minimizingthe backhaul energy consumption while satisfying users’ qualityof service (QoS) requirements on high data rate. The formulatedmixed integer non-linear programming (MINLP) problem issolved by decomposing it into two stages of subproblems. Inthe first stage, the convex optimization technique is applied totackle the coded caching subproblem. Subsequently, we proposetwo efficient algorithms based on matching in the second stageto deal with the transmission subproblem. Simulation resultsdemonstrate that the proposed schemes can effectively maximizethe backhaul energy saving and enhance the download ratecompared with the benchmark scheme.