Due to severe variation in load demand over time, utility companies generally raise electrical energy price during periods of high load demand. A grid-connected hybrid electrical energy storage (HEES) system can help residential users lower their electric bills by storing energy during low-price hours and releasing the stored energy during high-price hours. A HEES system consists of different types of electrical energy storage (EES) elements, utilizing the benefits of each type while hiding their weaknesses. This paper presents a residential energy management system to maximize the annual profits on residential electric bills, based on a HEES system comprised of a lead-acid battery bank as the main storage bank and a Li-ion battery bank as the energy buffer. We first derive the optimal daily energy management policy based on energy buffering to minimize the daily energy cost. Next, we find the near-optimal design specifications of the energy management system, aiming at maximizing the amortized annual profits under practical constraints. We show that this system achieves averagely 11.10% more profits compared to the none-buffering HEES system.