For unmanned aerial vehicle (UAV) aided millimeter wave (mmWave) networks, we propose a unified three-dimensional (3D) spatial framework in this paper to model a general case that uncovered users send messages to base stations via UAVs. More specifically, the locations of transceivers in downlink and uplink are modeled through the Poisson point processes and Poisson cluster processes (PCPs), respectively. For PCPs, Matern cluster and Thomas cluster processes, are analyzed. Furthermore, both 3D blockage processes and 3D antenna patterns are introduced for appraising the effect of altitudes. Based on this unified framework, several closed-form expressions for the coverage probability in the uplink and downlink, are derived. By investigating the entire communication process, which includes the two aforementioned phases and the cooperative transmission between them, tractable expressions of system coverage probabilities are derived. Next, three practical applications in UAV networks are provided as case studies of the proposed framework. The results reveal that the impact of thermal noise and non-line-of-sight mmWave transmissions is negligible. In the considered networks, mmWave outperforms sub-6 GHz in terms of the data rate, due to the sharp direction beamforming and large transmit bandwidth. Additionally, there exists an optimal altitude of UAVs, which maximizes the system coverage probability.