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This work develops microgrid dispatch algorithms with a unified approach to model predictive control (MPC) to (a) operate in grid-connected mode to minimize total operational cost, (b) operate in islanded mode to maximize resilience during a utility outage, and (c) utilize weighting factors in the grid-connected objective function to preserve islanded capability (on-site fuel reserves, battery state of charge) to enhance resilience in the potential event of an unplanned grid outage. Resilience is defined using microgrid survivability (probability to serve 100% of critical load), autonomy (duration of time to serve 100% of critical load), and unserved energy (curtailed critical load) for a target of 7 days during a grid outage. The developed methods are applied to a military microgrid with 2,250 kW of diesel generation, 3,450 kW/13,800 kWh battery storage, and 16,479 kW of solar photovoltaics. Sensitivity analysis is conducted to determine the selection of weighting factors to have the best impact on three developed objectives: grid-connected economics, islanded resilience, and carbon intensity. Optimal weighting factors reduce operating costs by 0.1%, increase survivability by 3.9%, increase autonomy by 16.7%, reduce unserved energy by 94.1%, and increase carbon intensity by 2.5%. [ABSTRACT FROM AUTHOR]