In heterogeneous cellular network (HCN), mobile users may travel across the coverage of different base stations (BSs). Handoff procedures need to be performed to maintain seamless connectivity. Since BSs in different tiers have distinct setting about transmission power and range extension bias, analysis for the network performance becomes complicated, particularly for the vertical handoff as an important functionality in HCN. To facilitate performance analysis, this letter proposes a method built on the equivalence between vertical handoff and horizontal handoff events. With the established equivalence, both types of handoff probabilities can be obtained in a single analytical framework. We also derive the coverage probability of mobile users by including the handoff cost in the analysis and obtain a compact expression. Numerical results are presented to validate the analysis accuracy and provide insights to the performance of HCN in supporting mobility.