This paper presents an approach for systematically modeling a class of microgrid (MG) systems. The derived model accommodates grid-connected and islanded operation of the MG simultaneously, and allows modeling of converter-based as well as directly interfaced resources. Full modeling of virtual synchronous machines and actual synchronous generators is addressed. The originally nonlinear model is then converted to a linear model whose eigenvalues determine local stability of the MG. The model is used to analyze impacts of cross-coupling droop terms on the MG stability. The conclusions of this analysis are as follows. Addition of cross-coupling droop terms reduces the losses, compromises the stability in the grid-connected mode, and improves the stability in standalone mode. Therefore, for an MG that is intended to continuously operate at grid-connected and standalone mode, only a modest amount of cross-coupling terms is recommended to increase the efficiency without compromising the grid-connected stability. Simulation and experimental results are presented to verify the derivations.