In a previous paper, a quantum-mechanical formulation involving both mean fields and independent-particle fields in many-fermion systems was proposed using the path-integral technique. Then the semiclassical calculation of the energy spectra was performed, and the quantization rule was derived by applying a stationary phase approximation on the path integral. In this paper, a boson-fermion expansion is derived from our formulation using Dirac quantization. As an illustration, the Lipkin model is utilized.