During bulk power system restoration, black-start (BS) units are used to crank non-BS units in such a way that the over system generation capability is maximized. However, traditional power system restoration methods rely on stationary BS units, whose number is limited due to high investment and geographic conditions, impeding a fast system restoration. To enhance restoration efficiency, this paper proposes an integrated power system parallel restoration method considering the support of mobile energy storage systems (MESSs), which can provide cranking power to non-BS units and transform them into MESS-assisted BS units. MESSs are routed and scheduled via transportation network, along with restoration planning in power network by integrating them into a mixed integrated linear programming model. Specifically, to describe the interactive behavior between MESSs and the power system, a mobility model for MESSs is proposed, which indicates the travel path, travel time and connection nodes. Then, an integrated optimization model involving BS unit location, zone partitioning, network reconfiguration and generator start-up is formulated. The proposed method was simulated in the modified IEEE 30-bus transmission system coupled with 11-node transportation system. The results show that, in contrast with a decoupled restoration method, the proposed method increases system generation capability by 6.3%.