Two-lane highways make up a substantial proportion of the road network in most of the world. Passing is among the most significant driving behaviors on two-lane highways. It substantially impacts the highway performance. Despite the importance of the problem, few studies attempted to model passing behavior. In this research, a model that attempts to capture both drivers' desire to pass and their gap acceptance decisions to complete a desired passing maneuver is developed and estimated using data on passing maneuvers collected with a driving simulator. Sixteen different scenarios were used in the experiment in order to capture the impact of factors related to the various vehicles involved, the road geometry and the driver characteristics in the model. A passing behavior model is developed that includes choices in two levels: the desire to pass and the decision whether or not to accept an available passing gap. The probability to complete a passing maneuver is modeled as the product of the probabilities of a positive decision on both these choices. The estimation results show that modeling the drivers' desire to pass the vehicle in front has a statistically significant contribution in explaining their passing behavior. The two sub-models incorporate variables that capture the impact of the attributes of the specific passing gap that the driver evaluates and the relevant vehicles, the geometric characteristics of the road section and the driver characteristics and account for unobserved heterogeneity in the driver population.