As popular mixed quantum-classical dynamics methods, trajectory surface hopping and Ehrenfest mean field have been widely utilized to simulate nonadiabatic dynamics. Recently, we have proposed the branching-corrected surface hopping and the branching-corrected mean field methods, both of which closely reproduce the exact quantum dynamics in a series of standard scattering models. Here, the mixed surface hopping and mean field with branching correction (BCSHMF) is presented as a unified framework of mixed quantum-classical dynamics. As benchmarked in thousands of diverse three-level and four-level scattering models, BCSHMF achieves high reliability and flexibility, implying that surface hopping and mean field are compatible with each other in nature, and trajectory branching is essential for the mixed quantum-classical description of nonadiabatic dynamics.