This paper is the first to present an efficient charge management algorithm focusing on extending the cycle life of battery elements in hybrid electrical energy storage (HEES) systems while simultaneously improving the overall cycle efficiency. In particular, it proposes to apply a crossover filter to the power source and load profiles. The goal of this filtering technique is to allow the battery banks to stably (i.e., with low variation) receive energy from the power source and/or provide energy to the load device, while leaving the spiky (i.e., with high variation) power supply or demand to be dealt with by the supercapacitor banks. To maximize the HEES system cycle efficiency, a mathematical problem is formulated and solved to determine the optimal charging/discharging current profiles and charge transfer interconnect voltage, taking into account the power loss of the EES elements and power converters. To minimize the state of health (SoH) degradation of the battery array in the HEES system, we make use of two facts: the SoH of battery is better maintained if (i) the SoC swing is smaller, and (ii) the same SoC swing occurs at lower average SoC. Now then using the supercapacitor bank to deal with the high-frequency component of the power supply or demand, we can reduce the SoC swing for the battery array and lower the SoC of the array. A secondary helpful effect is that, for fixed and given amount of energy delivered to the load device, an improvement in the overall charge cycle efficiency of the HEES system translates into a further reduction in both the average SoC and the SoC swing of the battery array. The proposed charge management algorithm for a Li-ion battery - supercapacitor bank HEES system is simulated and compared to a homogeneous EES system comprised of Li-ion batteries only. Experimental results show significant performance enhancements for the HEES system, an increase of up to 21.9% and 4.82x in terms of the cycle efficiency and cycle life, respectively.