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This paper proposes a security-constrained distribution system market clearing model in presence of proactive customers, and in particular, microgrids. This problem is solved by a distribution system operator (DSO) which acts as a market-driven distribution management entity. The system security consists of distribution line outage as well as microgrid islanding. None of these two security events are in the control of the DSO, so associated uncertainties are considered in the problem modeling. Moreover, the interdependency of the microgrid islanding to distribution line outages is taken into account. Numerical simulations on the IEEE 33-bus standard test system exhibit the significance and the effectiveness of the proposed model.