High-power pulsed loads (PPL) present significant challenges for the design of aircraft power systems. A hybrid power system (HPS) comprising batteries and supercapacitors, integrated with the existing generators, shows promise as a solution. However, optimizing the proportions of different energy storages is critical for minimizing system weight and maximizing efficiency. To address this challenge, this study proposes a serial-nested co-optimization design method. This approach optimizes energy types, component capacities and voltage levels, as well as power allocations considering PPL characteristics. To achieve this end, relationships between PPL parameters and energy configuration are established by analyzing the spectrum characteristics of PPL. These nonlinear relationships provide a universal configuration criteria, represented by a response surface calculated via Design of Experiment (DoE) data. To strike a balance between system weight and efficiency, multidisciplinary design models for each component are developed. A multilevel optimization design method is proposed, enabling simultaneous system-level and component-level co-design. Extensive simulations validate the effectiveness of the proposed co-optimization approach. Optimization results of four power distribution strategies across two architectures are compared to obtain optimal HPS solutions that meet requirements of an aircraft load profile.E.