This article proposes a method of predicting the influence of random load behavior on the dynamics of dc microgrids and distribution systems. This is accomplished by combining stochastic load models and deterministic microgrid models. Together, these elements constitute a stochastic hybrid system. The resulting model enables straightforward calculation of dynamic state moments, which are used to assess the probability of desirable operating conditions. Specific consideration is given to systems based on the dual active bridge (DAB) topology. Bounds are derived for the probability of zero voltage switching (ZVS) in DAB converters. A simple example is presented to demonstrate how these bounds may be used to improve ZVS performance as an optimization problem. Predictions of state moment dynamics and ZVS probability assessments are verified through comparisons to Monte Carlo simulations.