Seismically retrofitting reinforced concrete (RC) building with a combination of buckling-restrained braces (BRBs) and elastic steel frames offers a practical solution that provides additional lateral stiffness and energy dissipation capacity. However, the available methods to vertically distribute the BRB sizes based on equivalent linearization do not consider the additional stiffness due to the composite behavior between the RC frame and the elastic steel frame, which may lead to an overly conservative estimate of the BRB stiffness demands. This study proposes a retrofit design method incorporating the composite behavior. Numerical models considering the detailed composite behavior are developed and calibrated against quasi-static cyclic loading tests, and a simplified evaluation method is proposed. A four-story RC school building is used as a benchmark model, and the proposed retrofit design method is validated using nonlinear response history analysis. The analysis results suggest that taking the composite behavior into account by using the proposed retrofit design method more accurately estimates the lateral stiffness of the retrofitted structure and leads to a more economic retrofit.