In recent years, there have been significant changes in power systems due to the integration of renewables, distributed generation, switched power loads, and energy storage systems, etc. Locally these AC/DC microgrids include both DC generation (such as solar PV) and AC generation (such as wind generation), various DC and AC loads, converters and inverters, and energy storage systems, such as storage batteries and supercapacitors. DC systems are often characterized as low inertia systems whereas AC generation and systems are usually high inertia and high time constant systems. As such, various components of the microgrid will have different temporal characteristics in case of disturbances, such as short circuit, load switchings, etc. which may lead to instability of the microgrid. This research develops the first principle model for coupling the AC and the DC subsystem of an integrated AC/DC microgrid utilizing the dq-framework. The developed model is highly nonlinear and captures the dynamic interaction between the AC and DC subsystems of the microgrid. Lyapunov stability is used to evaluate the stability of the complete system. Simulation results show that the AC and DC subsystems are tightly dynamically coupled so that any disturbance in one subsystem induces transients in the other subsystem. Induced transients due to pulse loads on the AC and DC subsystems clearly show that generator damper winding alone may not be enough to mitigate transients in the microgrid. Addition of prime mover and excitation system controllers for the generator improves the transients primarily on the AC subsystem. Thus, a battery storage with a charge/discharge controller was also added to the DC subsystem. Simulations of the AC/DC microgrid with all three controllers validate the smooth operation of the system for all types of disturbances. The proposed method can be extended in modeling microgrid with multiple generators and various types of loads.