Integration of heterogeneous models can achieve interconnection between multiple types of simulation systems and realize reusability of model components. Recently data-driven modeling is becoming more and more common with the popularity of machine learning. It is a representative of black-box models which are totally dependent on data and need no disciplinary knowledge. From this perspective, models can be divided into white-box models, grey-box models and black-box models. Few researchers have considered the integrated issue under this mode. In this paper, we propose an integrated framework for scenarios where white-box models and black-box models are both involved. We discuss the structures of corresponding proxy models and then introduce a modified advancing strategy for general optimistic methods. It can greatly avoid possible rollback for black-box models and achieve efficient simulation by adjustment of simulation sequence.