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Millimeter wave (mmWave) small-cell networks can provide high regional throughput, but the backhaul requirement has become a performance bottleneck. This paper proposes a hybrid system that combines traditional backhaul-connected small base stations (SBSs) and cache-enabled SBSs to achieve the maximum area spectral efficiency (ASE) while saving backhaul consumption in mmWave small cell networks. We derive and compare the ASE results for both the traditional and hybrid networks, and also show that the optimal content placement to maximize ASE is to cache the most popular contents. Numerical results demonstrate the performance improvement of deploying cache-enabled SBSs. Furthermore, given a total caching capacity, it is revealed that there is a tradeoff between the cache-enabled SBSs density and individual cache size to maximize the ASE.