Business process modeling is an important topic of enterprise modeling. Modeling process can help us to define new process, evaluate and improve existing ones. As the development of Internet and B2B commerce, business partnerships are being fostered in order to broaden the scope of their market. Business process thus has been scatted over multiple organizations. At the same time, each participant of the cooperation has their own private process. So how to define and model cross-organizational process while keep each participant?s autonomy poses new challenge to us. In this paper, we will focus on two problems:1) How can we guarantee the private process of each participant is consistent to the coordination protocol specified by Message Sequence Charts? 2) How can we formalize the execution of the interaction protocol, which means the execution of private processes conforms to the interaction protocol? An approach based on Object Petri net and behavior inheritance will be proposed in this paper to solve the above two problems.