A tractable stochastic geometry model is proposed to characterize the performance of the novel point-to-multipoint (P2MP) assisted backhaul networks with millimeter wave (mmWave) capability. The novel performance analysis is studied based on the general backhaul network (GBN) and the simplified backhaul network (SBN) models. To analyze the signal-to-interference-plus-noise ratio (SINR) coverage probability of the backhaul networks, a range of the exact- and closed-form expressions are derived for both the GBN and SBN models. With the aid of the tractable model, the optimal power control algorithm is proposed for maximizing the trade-off between energy-efficiency (EE) and area spectral-efficiency (ASE) for the mmWave backhaul networks. The analytical results of the SINR coverage probability are validated, and they can match those obtained from Monte-Carlo experiments. Our numerical results for ASE performance demonstrate the significant effectiveness of our P2MP architecture over the traditional point-to-point (P2P) setup. Moreover, our P2MP mmWave backhaul networks are able to achieve dramatically higher rate performance than that obtained by the ultra high frequency (UHF) networks. Furthermore, to achieve the optimal EE and ASE trade-off, the mmWave backhaul networks should be designed to limit the link distances and line-of-sight (LOS) interferences while optimizing the transmission power.