We conduct novel coverage probability analysis of downlink transmission in a three-dimensional (3D) terahertz (THz) communication (THzCom) system. In this system, we address the unique propagation properties in THz band, e.g., absorption loss, super-narrow directional beams, and high vulnerability towards blockage, which are fundamentally different from those at lower frequencies. Different from existing studies, we characterize the performance while considering the effect of 3D directional antennas at both access points (APs) and user equipments (UEs), and the joint impact of the blockage caused by the user itself, moving humans, and wall blockers in a 3D environment. Under such consideration, we develop a tractable analytical framework to derive a new expression for the coverage probability by examining the regions where dominant interferers (i.e., those can cause outage by themselves) can exist, and the average number of interferers existing in these regions. Aided by numerical results, we validate our analysis and reveal that ignoring the impact of the vertical heights of THz devices in the analysis leads to a substantial underestimation of the coverage probability. We also show that it is more worthwhile to increase the antenna directivity at the APs than at the UEs, to produce a more reliable THzCom system.