Using tools from stochastic geometry, this paper develops a tractable framework to analyze the performance of a mobile user in a two-tier wireless network operating on sub-6GHz and terahertz (THz) transmission frequencies. Specifically, using an equivalence distance approach, we characterize the overall handoff (HO) probability in terms of the horizontal and vertical HO and mobility-aware coverage probability. In addition, we characterize novel coverage probability expressions for THz network in the presence of molecular absorption noise and highlight its significant impact on the users' performance. Specifically, we derive a novel closed-form expression for the Laplace Transform of the cumulative molecular noise and interference observed by a mobile user in a hybrid RF-THz network. Furthermore, we provide a novel approximation to derive the conditional distance distributions of a typical user in a hybrid RF-THz network. Finally, using the overall HO probability and coverage probability expressions, the mobility-aware probability of coverage has been derived in a hybrid RF-THz network. Our mathematical results validate the correctness of the derived expressions using Monte-Carlo simulations. The results offer insights into the adverse impact of users' mobility and molecular noise in THz transmissions on the probability of coverage of mobile users. Our results demonstrate that a small increase in the intensity of terahertz base-stations (TBSs) (about 5 times) can increase the HO probability much more compared to the case when the intensity of RF BSs (RBSs) is increased by 100 times. Furthermore, we note that high molecular absorption can be beneficial (in terms of minimizing interference and molecular noise) for specific deployment intensity of TBSs and the benefits can outweigh the drawbacks of signal degradation due to molecular absorption.