This paper aims to exploit the fundamental limits on the downlink coverage and spatial throughput performances of a cellular network comprised of a tier of unmanned aerial vehicle (UAV) base stations (BSs) using the millimeter wave (mmWave) band and a tier of ground BSs using the ultra high frequency (UHF) band. To reduce handover signaling overhead, the ground BSs take charge of control signaling delivery whereas the UAVs are in charge of payload data transmission so that users need to be simultaneously associated with a ground BS and a UAV in this network with a control-data plane-split architecture. We first propose a three-dimensional (3D) location distribution model of the UAVs using stochastic geometry which is able to generally characterize the positions of the UAVs in the sky. Using this 3D distribution model of UAVs, two performance metrics, i.e., multi-cell coverage probability and volume spectral efficiency, are proposed. Their explicit low-complexity expressions are derived and their upper limits are found when each of the UAVs and ground BSs is equipped with a massive antenna array. We further show that the multi-cell coverage probability and the volume spectral efficiency can be maximized by optimally deploying and positioning the UAVs in the sky and thereby their fundamental maximal limits are found. These important analytical findings are validated by numerical simulations.