With the development of microgrids (MGs), interconnected operation of multiple MGs is becoming a promising strategy for the smart grid. In this paper, a privacy-preserving distributed optimal scheduling method is proposed for the interconnected microgrids (IMG) with a battery energy storage system (BESS) and renewable energy resources (RESs). The optimal scheduling problem is modeled to minimize the coalitional operation cost of the IMG, including the fuel cost of conventional distributed generators and the life loss cost of BESSs. By using the framework of the alternating direction method of multipliers (ADMM), a distributed optimal scheduling model and an iteration solution algorithm for the IMG is introduced; only the expected exchanging power (EEP) of each MG is required during the iterations. Furthermore, a privacy-preserving strategy for the sharing of the EEP among MGs is designed to work with the mechanism of the distributed algorithm. According to the security analysis, the EEP can be delivered in a cooperative and privacy-preserving way. A case study and numerical results are given in terms of the convergence of the algorithm, the comparison of the costs and the implementation efficiency.