Heterogeneous nature of the vehicular networks, which results from the co-existence of human-driven, semi-automated, and fully autonomous vehicles, is a challenging phenomenon toward the realization of the intelligent transportation systems with an acceptable level of safety, comfort, and efficiency. Safety applications highly suffer from communication resource limitations, specifically in dense and congested vehicular networks. The idea of model-based communication (MBC) has been recently proposed to address this issue. In this work, we propose Gaussian Process-based Stochastic Hybrid System with Cumulative Relevant History (CRH-GP-SHS) framework, which is a hierarchical stochastic hybrid modeling structure, built upon a non-parametric Bayesian inference method, i.e. Gaussian processes. This framework is proposed in order to be employed within the MBC context to jointly model driver/vehicle behavior as a stochastic object. Non-parametric Bayesian methods relieve the limitations imposed by non-evolutionary model structures and enable the proposed framework to properly capture different stochastic behaviors. The performance of the proposed CRH-GP-SHS framework at the inter-mode level has been evaluated over a set of realistic lane change maneuvers from NGSIM-US101 dataset. The results show a noticeable performance improvement for GP in comparison to the baseline constant speed model, specifically in critical situations such as highly congested networks. Moreover, an augmented model has also been proposed which is a composition of GP and constant speed models and capable of capturing the driver behavior under various network reliability conditions.