In this paper, an operational scheme is developed for DC microgrids in coordination with existing AC grids using nonlinear backstepping controllers. The proposed operational scheme is designed to maintain the voltage stability of DC microgrids as well as to provide ancillary services to the AC grid by supplying excess power to AC loads. At the same time, the proposed scheme also ensures the power balance within DC microgrids by consuming power from AC grids when there are power shortages. The microgrid structure in this paper comprises a solar photovoltaic (PV) unit, permanent magnet synchronous generator (PMSG)-based wind generation system, and batter energy storage system (BESS) with AC and DC loads. A bi-directional DC-DC converter is used with the BESS in order to maintain the supply-demand balance within the DC microgrid through charging and discharging. Similarly, a bi-directional voltage source converter (VSC) with an LC filter on the AC-side is used to manage the power flow between the DC microgrid and AC grid. The nonlinear backstepping controllers are used to control all converters within the proposed microgrid structure where these controllers are designed based on the dynamical models of different components. Control Lyapunov functions (CLFs) are used to analyze the overall stability of the microgrid and simulation studies are carried out to validate the performance of the proposed operational scheme under different operating conditions. Simulation results are also compared with an existing nonlinear sliding mode controller (SMC)-based operational scheme in order to demonstrate the superiority of the proposed scheme.