An integrated energy community with a distributed utilization of renewable energy and complementary electricity–gas–cold–heat integrated energy will play an important role in energy conservation and emission reduction. In addition, compared with traditional thermoelectric power equipment, solid oxide fuel cells have many advantages, such as a high energy utilization rate, good waste heat quality, and low carbon emissions. Therefore, the SOFC-based multi-energy and energy storage sharing operation model of an integrated energy community with an electricity–gas–cooling–heat integrated energy system is constructed, and a bi-objective optimal configuration model considering the carbon emission index is established. Considering the economic objective of the smallest annual total operating cost as the most important objective in optimizing the planning model, the ε-constraint method is used to transform the environmental objective function with the