This paper presents a multi-objective optimization formulation for designing domestic cogeneration systems to satisfy thermal and electric energy demands. The proposed model is formulated as a multi-objective mixed-integer nonlinear programming model, which incorporates as economic objective function the minimization of the total annual cost, which includes the capital costs for the new units and the thermal storage system as well as the operating and maintenance costs. The model also incorporates an environmental objective function, which accounts for the life cycle assessment through the Eco-indicator 99 method to account for the damages to the resources, human health, and ecosystem quality. The proposed model allows considering the interaction with the external users and the external electric grid. The optimization formulation is solved to generate design alternatives to establish tradeoffs among the considered objectives.