A microscopic theory of the spin Peltier effect in a bilayer structure comprising a paramagnetic metal (PM) and a ferromagnetic insulator (FI) based on the nonequilibrium Green's function method is presented. Spin current and heat current driven by temperature gradient and spin accumulation are formulated as functions of spin susceptibilities in the PM and the FI, and are summarized by Onsager's reciprocal relations. By using the current formulas, we estimate heat generation and absorption at the interface driven by the heat-current injection mediated by spins from PM into FI.