Modern buildings and their HVAC systems are required to be not only energy-efficient but also produce fewer economical and environmental impacts while adhering to an ever-increasing demand for better environment. Research shows that building regulations which depend mainly on building envelope requirements do not guarantee the best environmental and economical solutions. In the current study, a modified multi-objective optimization approach based on Genetic Algorithm is proposed and combined with IDA ICE (building performance simulation program). The combination is used to minimize the carbon dioxide equivalent (CO2-eq) emissions and the investment cost for a two-storey house and its HVAC system. Heating/cooling energy source, heat recovery type, and six building envelope parameters are considered as design variables. The modified optimization approach performed efficiently with the three studied cases, which address different summer overheating levels, and a set of optimal combinations (Pareto front) was achieved for each case. It is concluded that: (1) compared with initial design, 32% less CO2-eq emissions and 26% lower investment cost solution could be achieved, (2) the type of heating energy source has a marked influence on the optimal solutions, (3) the influence of the external wall, roof, and floor insulation thickness as well as the window U-value on the energy consumption and thermal comfort level can be reduced into an overall building U-value, (4) to avoid much of summer overheating, dwellings which have insufficient natural ventilation measures could require less insulation than the standard (inconsistent with energy saving requirements) and/or additional cost for shading option.