A general fully microscopic theory for interacting fermion—boson systems is presented with an explicit treatment for the single-fermion case. The broken-pair approximation (BPA) is applied to generate correlated fermion pairs. Using these and an odd fermion the boson and the ideal-fermion images are constructed by employing modified Marumori and Dyson mappings. Various problems like the renormalization effects, spurious solutions and the non-hermiticity encountered in practical calculations are discussed. Explicit expressions for calculating the parameters of the hamiltonian of the phenomenological interacting fermion-boson model are derived.