This research addresses the challenge of optimizing hybrid heating systems (HHS) that combine heat pumps with natural gas boilers in residential buildings. Existing buildings primarily rely on high-temperature natural gas boilers, limiting the adoption of more efficient, low-temperature alternatives like heat pumps. The research aims to explore the most effective hydraulic configurations for HHS with the goal of minimize energy usage, primary energy cost and CO₂ emissions while maintaining comfort levels. A MATLAB-based simulation model was developed to compare various HHS configurations under a unified control strategy over an annual cycle. The configurations studied included a base system with only a natural gas boiler and hybrid systems with series, parallel, and buffer tank arrangements. The results indicate that all hybrid configurations substantially outperform the boiler-only system in terms of energy efficiency and emissions reduction. The series hybrid system emerged as the most efficient, reducing energy usage to 59% of the boiler-only system, with the parallel system close behind at 58%. The buffer tank system, while less efficient than the other hybrids, still achieved a 49% reduction in energy usage compared to the boiler-only setup. Cost analysis revealed a primary energy cost reductions of 17% for both the series and parallel system and 4% for the system with buffer tank. CO₂ emissions were reduced by 46% to 56% across the hybrid configurations. The study highlights the critical role of control strategies over hydraulic configurations, as the series and parallel systems showed very similar performance. However, incorporating more components, especially storage like buffer tanks, negatively impacted overall efficiency. Real-world performance may differ slightly due to unaccounted changes in boiler efficiency from flue gas condensation, but the impact is expected to be modest. This research provides valuable insights for optimizing hybrid heating technologies in residential buildings, with implications for broader applications in other building types. The significant energy and cost savings, along with substantial CO₂ emission reductions, present a compelling case for adopting hybrid heating systems in energy retrofits and new constructions. The findings support global climate action and energy efficiency goals, contributing to environmental sustainability and energy security.