Microscopic traffic flow models enable predictions of traffic operations, which allows traffic engineers to assess the efficiency and safety effects of roadway designs. Modeling vehicle trajectories inside intersections is challenging because there is an infinite number of possible paths in a two-dimensional space, and drivers can simultaneously adapt their speeds as well. To date, human driver models for simultaneous longitudinal and lateral vehicle control based on the infrastructure characteristics and interactions with other drivers inside an intersection are still lacking. The contribution of this paper is threefold. First, it proposes an integrated microscopic traffic flow model to describe human-driven vehicle maneuvers under interactions. Drivers plan their heading and acceleration in the predicted future to minimize costs representing undesirable situations. The model works with a joint optimization for an interaction cost term. The weights associated with the interaction cost reflect how selfish or altruistic drivers are. Second, the proposed model endogenously gives the order of vehicles in case of crossing paths. Third, the paper develops a clustered validation method for microscopic traffic flow models with interacting vehicles, which account for interdriver variations. Results show that the model can accurately describe vehicle passing orders of interacting maneuvers, paths, and speeds against empirical data. The model can be applied to assess various intersection designs.