Abstract: Vertical height growth of hydraulic fractures (HFs) can unexpectedly penetrate a stratigraphic interface and propagate into neighboring layers, thereby resulting in low gas-production efficiency and high risk of groundwater contamination or fault reactivation. Understanding of hydraulic fracture behavior at the interface is of pivotal importance for the successful development of layered reservoirs. In this paper, a two-dimensional analytical model was developed to examine HF penetration and termination behavior at an orthogonal interface between two dissimilar materials. This model involves changes in the stress singularity ahead of the HF tip, which may alter at the formation interface due to material heterogeneity. Three critical stress conditions were considered to assess possible fracture behavior (i.e., crossing, slippage, and opening) at the interface. Then, this model was verified by comparing its theoretical predictions to numerical simulations and three independent experiments. Good agreement with the simulation results and experimental data was observed, which shows the validity and reliability of this model. Finally, a parametric study was conducted to investigate the effects of key formation parameters (elastic modulus, Poisson's ratio, and fracture toughness) between adjacent layers. These results indicate that the variation in the introduced parameters can limit or promote vertical HF growth by redistributing the induced normal and shear stresses at the interface. Among the three studied parameters, Poisson's ratio has the least influence on the formation interface. When the fracture toughness and elastic modulus of the bounding layer are larger than those of the pay zone layer, the influence of fracture toughness will dominate the HF behavior at the interface; otherwise, the HF behavior will more likely be influenced by elastic modulus.