An integrated energy system (IES) can yield several benefits in energy, environmental impacts, cost, and flexibility over a separate system, although the initial cost may be higher. An IES using gas turbine, solar photovoltaics (PV), heat pumps, electrical cooling, and energy storage units is proposed here to satisfy the electricity, cooling, and heating demands of a residential building. A multi-objective optimization approach is used to find the best solutions considering energy, supply-demand matching and exergo-environmental economic indices with life cycle assessment (LCA) in following electric mode. The maximum benefit from the IES studied is reached with a system yielding 53.08% for energy savings, 99.88% matching, and 43.50% cost savings. The ideal scheme selected by the TOPSIS method has a higher annual total cost than the cost with conventional method, but has a better cost saving ratio, 41.81%. A sensitivity analysis shows that a higher PV use would decrease the fuel consumption, but it would reduce the matching and economic performance. Similar to the effect of natural gas price, the off-grid electricity price has higher impact on the cost saving ratio, but lower influence on the specific exergo-environmental cost.