This paper develops a multi-objective co-design optimization framework for the optimal sizing and selection of battery and power electronics in hybrid battery energy storage systems (HBESSs) connected to the grid. The co-design optimization approach is crucial for such a complex system with coupled subcomponents. To this end, a nondominated sorting genetic algorithm (NSGA-II) is used for optimal sizing and selection of technologies in the design of the HBESS, considering design parameters such as cost, efficiency, and lifetime. The interoperable framework is applied considering three first-life battery cells and one second-life battery cell for forming two independent battery packs as a hybrid battery unit and considers two power conversion architectures for interfacing the hybrid battery unit to the grid with different power stages and levels of modularity. Finally, the globally best HBESS system obtained as the output of the framework is made up of LTO first-life and LFP second-life cells and enables a total cost of ownership (TCO) reduction of 29.6% compared to the baseline.