Climate change and the associated global warming raise the possibility of weather-related natural disasters. Power outages due to natural catastrophes cause substantial financial loss. Moreover, an uninterrupted power supply is essential in disaster-prone areas to continue rescue and other humanitarian activities. Therefore, energy systems must be resilient to withstand power outages due to natural events. Resilience and enhancement techniques, and schemes of integrated electricity and microgrids’ heat demand during power outages, were mainly overlooked in the earlier analysis. Therefore, this analysis aims to analyze a grid-tied microgrid’s survivability during a power outage due to a natural disaster in Texas, USA. Mixed-integer linear programming (MILP) is used to optimize various energy resources, such as PV, battery, grid, and combined heat and power (CHP) for Texas, USA. These technologies were run in an outage condition to observe their resiliency benefits. To determine the resilience performance of the CHP/PV/battery system for the hospital building, a new probabilistic approach was applied. A 24-h outage was simulated in REopt lite software, and this study found that the PV/battery/CHP system could easily withstand the outage. The optimum system consists of 3933 kW of PV, 4441 kWh of storage, and a CHP unit having a capacity of 208 kW. The proposed microgrid emits 79.81% less CO2 than the only grid system. The microgrid has a net benefit of $1,007,204 over the project duration. The introduction of the proposed microgrid will bring about life-cycle savings (LCS) of 37.02 million USD over the project’s lifespan.