An optimal structural design model of residential power and heat supply devices (R-PHDs), including cogeneration and heat pump units, was developed by considering their operational and capital recovery constraints. The structure of R-PHDs with peripheral devices, sizes of energy storage devices, and their multi-period operation were determined so as to minimize annual primary energy consumption. In addition to various operational constraints for a cogeneration unit and a battery unit, an operable-hours constraint and daily selection of outlet water temperature were newly formulated for heat pump units. The capital recovery by reducing energy cost was also considered in order to select R-PHDs that have high energy-saving effects but are presently expensive. The developed model took the form of a mixed-integer linear programming problem. The model was applied to the structural design of R-PHDs, whose candidates are three types of cogeneration units (gas engine, polymer electrolyte fuel cell, and solid oxide fuel cell), heat pump unit, storage tank, battery unit, and peripheral devices. The result revealed a trade-off between energy savings and initial cost in the optimal structures. A sensitivity analysis of the initial costs of expensive devices was also carried out to clarify their initial cost targets.