This paper presents a comprehensive analysis of the joint distribution of electrical and thermal energy in a smart home connected to a microgrid integrating renewable resources, combined heat and power (CHP) units, and storage systems. While most existing studies have primarily focused on generation planning and storage management, fewer works have examined the simultaneous optimization of electricity and heat flows in residential environments. To address this gap, a mixed-integer linear programming (MILP) model is developed to schedule household appliances and manage load shifting according to time-varying electricity prices, heating demand, and demand profiles, and the optimization is solved using MATLAB tools. The proposed framework is applied to a residential complex of 10 and 20 households under different CHP capacities and demand scenarios. Simulation results reveal that increasing CHP capacity from 5 kW to 20 kW significantly improves the coordination of electrical and thermal distribution, reduces reliance on the main grid, and lowers boiler operation, thereby enhancing overall efficiency. Additional analyses with different numbers of households confirm the scalability of the model, ensuring stable performance under varying load levels. A comparative scenario without microgrid integration further highlights the substantial benefits of the proposed system in reducing operational costs and improving resilience. To address this gap, a unified MILP jointly schedules electrical–thermal resources (CHP, renewables, and dual electrical/thermal storage) and employs a price–energy iterative scheme with explicit fairness constraints, ensuring no household is worse off than in non-cooperative operation. These results demonstrate that the coordinated consideration of both power and heat flows provides a more holistic strategy for smart home energy management than electricity-only approaches. In 24-h studies, increasing installed CHP capacity from 5 to 100 kW reduced total operating cost from $379.68 to $191.52 (≈49.6%). By integrating demand response (DR) programs with CHP and renewable resources, the proposed method reduces energy costs, strengthens supply security, and contributes to the sustainability of residential microgrids.