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Modeling stochastic traffic behaviors at the microscopic level, such as car-following and lane-changing, is a crucial task to understand the interactions between individual vehicles in traffic streams. Leveraging a recently developed theory named physics regularized Gaussian process (PRGP), this study presents a stochastic microscopic traffic model that can capture the randomness and measure errors in the real world. Physical knowledge from classical car-following models is converted as physics regularizers, in the form of shadow Gaussian process (GP), of a multivariate PRGP for improving the modeling accuracy. More specifically, a Bayesian inference algorithm is developed to estimate the mean and kernel of GPs, and an enhanced latent force model is formulated to encode physical knowledge into stochastic processes. Also, based on the posterior regularization inference framework, an efficient stochastic optimization algorithm is developed to maximize the evidence lower-bound of the system likelihood. To evaluate the performance of the proposed models, this study conducts empirical studies on real-world vehicle trajectories from the NGSIM dataset. Since one unique feature of the proposed framework is the capability of capturing both car-following and lane-changing behaviors with one single model, numerical tests are carried out with two separated datasets, one contains lane-changing maneuvers and the other doesn't. The results show the proposed method outperforms the previous influential methods in estimation precision.