<p>This work derives the sixteen effective moduli of fibrous piezoelectric-piezomagnetic composites with imperfect interfaces in a unified fashion based on the composite cylinder assemblage model. The imperfect interface is described by generalized interface stress model to be generally anisotropic with the fully coupled magneto-electro-elastic behavior. Afterwards, two different sets of exact relations between the sixteen effective moduli are formulated as the extensions of Hill and Milgrom-Shtrikman relations, respectively. Although the effective moduli with imperfect interfaces have been found to violate the Milgrom-Shtrikman relation in the literature, they are shown to satisfy a modified Milgrom-Shtrikman relation with imperfect interfaces. Moreover, using the technique of congruent transformation, the effective moduli of multiferroic composites with imperfect interfaces in coupled magnetic-electro-elastic case are obtained indirectly from available results in the uncoupled case, which coincide with those obtained by Mori–Tanaka model and generalized self-consistent model in the literature.</p>