An approach for modeling solar flare high-energy emissions is developed in which both thermal and nonthermal particles coexist and contribute to the radiation. The thermal/nonthermal distribution function is interpreted physically by postulating the existence of DC sheets in the flare region. The currents then provide both primary plasma heating through Joule dissipation, and runaway electron acceleration. The physics of runaway acceleration is discussed. Several methods are presented for obtaining approximations to the thermal/nonthermal distribution function, both within the current sheets and outside of them. Theoretical hard x ray spectra are calculated, allowing for thermal bremsstrahlung from the heated plasma electrons impinging on the chromosphere. A simple model for hard x ray images of two-ribbon flares is presented. Theoretical microwave gyrosynchrotron spectra are calculated and analyzed, uncovering important new effects caused by the interplay of thermal and nonthermal particles. The theoretical spectra are compared with observed high resolution spectra of solar flares, and excellent agreement is found, in both hard x rays and microwaves. The future detailed application of this approach to solar flares is discussed, as are possible refinements to this theory.