The scarcity of spectrum resources in current wireless communication systems has sparked enormous research interest in the terahertz (THz) frequency band. This band is characterized by fundamentally different propagation properties resulting in different interference structures from what we have observed so far at lower frequencies. In this paper, we derive a new expression for the coverage probability of downlink transmission in THz communication systems within a three-dimensional (3D) environment. First, we establish a 3D propagation model which considers the molecular absorption loss, 3D directional antennas at both access points (APs) and user equipments (UEs), interference from nearby APs, and dynamic blockages caused by moving humans. Then, we develop a novel easy-to-use analytical framework based on the dominant interferer analysis to evaluate the coverage probability, the novelty of which lies in the incorporation of the instantaneous interference and the vertical height of THz devices. Our numerical results demonstrate the accuracy of our analysis and reveal that the coverage probability significantly decreases when the transmission distance increases. We also show the increasing blocker density and increasing AP density impose different impacts on the coverage performance when the UE-AP link of interest is in line-of-sight. We further show that the coverage performance improvement brought by increasing the antenna directivity at APs is higher than that brought by increasing the antenna directivity at UEs.