The wide range of performance characteristics of storage technologies motivates the use of a hybrid energy storage system (HESS) that combines the best features of multiple technologies. However, HESS design is complex, in that it involves the choice of storage technologies, the sizing of each storage element, and deciding when to charge and discharge each underlying storage element (operating strategy). We formulate the problem of jointly optimizing the sizing and the operating strategy of an HESS that can be used for a large class of applications and storage technologies. Instead of a single set of storage element sizes, our approach determines the Pareto-optimal frontier of the sizes of the storage elements along with the corresponding optimal operating strategy. Thus, as long as the performance objective of a storage application (such as an off-grid microgrid) can be expressed as a linear combination of the underlying storage sizes, the optimal vector of storage sizes falls somewhere on this frontier. We present two case studies to illustrate our approach, demonstrating that a single storage technology is sometimes inadequate to meet application requirements, unlike an HESS designed using our approach. We also find simple, near-optimal, and practical operating strategies for these case studies, which allows us to gain several new engineering insights.