This paper studies the online dynamic security assessment (DSA) of future distribution systems in which multiple electrically coupled microgrids are operated as an interconnection. By leveraging the highly controllable power-electronics-based interfaces, we propose a novel interface control strategy for desirable load sharing among interconnected microgrids. Under such a control framework, theoretical results on system-wide stability criteria in the sense of Lyapunov are obtained. Potential application of these results for microgrid-based smart distribution system DSA is presented. Minimum information exchange is required among microgrid modules and the distribution system operator, which is a highly desirable feature in future distribution management systems. Numerical studies of a five-microgrid study system designed based on the IEEE 123-node test feeder show the effectiveness of the proposed control strategy and DSA framework.