UAVs and millimeter communications are considered as key technologies in the future wireless network that requires ultra-high data rates and seamless communication coverage expansion. In particular, since the terrestrial network is expected to be densified due to a myriad of small cells in B5G/6G, vertical mmWave backhauls using aerial platforms are attracting huge attention. Meanwhile, non-orthogonal multiple access (NOMA) is also being investigated as a next-generation multiple access technique due to its high spectral efficiency. In this paper, we present modeling and analysis of the UAV-aided mmWave backhaul/NOMA network. Taking the elaborate backhauls and access channels into consideration, we formulate an optimization problem in which UAV's position, transmit power and decoding orders are optimized for the maximum end-to-end network throughput. To solve the mixed-integer non-convex problem, we propose an iterative algorithm that can obtain a sub-optimal solution efficiently. Our numerical results show that the optimal deployment of UAV depends on the backhaul link state. In addition, it is shown that the proposed algorithm achieves up to 40% higher end-to-end network throughputs than other benchmark schemes.