A practical challenge facing the adoption of self-driving vehicles is the complex influence of the lateral dimension in vehicle traffic. This phenomenon has received little attention in the literature and few quantitative descriptions of interactions between vehicles are available for model validation. This paper proposes an analysis of the kinematic variables describing vehicle interactions on both axes during overtaking maneuvers using linear as well as nonlinear and nonparametric models based on real-world highway data. The principal findings are as follows: (a) a mutual influence between pairs of vehicles, especially at small lateral separation distances; (b) the higher the longitudinal velocity, the greater the lateral distances, no doubt to avoid collisions; and (c) lateral accelerations that tend to narrow lateral distance are associated with longitudinal accelerations that tend to widen it. These results are consistent across the different models applied and also with previous studies.