In this work, approximation schemes are developed to estimate the effective conductivity or resistivity of composites made of several phases with imperfect interfaces. The interface can be either highly conducting or resistive, and the constituent phases can be anisotropic. By using a generalized Eshelby's tensor accounting for imperfect interfaces and by applying the dilute distribution, Mori-Tanaka, self-consistent and generalized self-consistent schemes while incorporating imperfect interfaces between the inhomogeneity and matrix phases, the closed-form expressions for the effective conductivity and resistivity tensors are obtained. With the help of the dilute solution results for an inhomogeneity embedded in an effective medium matrix via an imperfect interface, the differential scheme is extended to predicting the effective conductivity and resistivity tensors. The estimations obtained by the differential scheme for the effective conductivity and resistivity are shown to comply with the generalized Hashin-Shtrikman bounds. Numerical results are provided to illustrate the dependence of the effective conductivity on the size and orientation distribution of inhomogeneities and to compare the estimations with the relevant upper and lower bounds. (C) 2012 Elsevier Ltd. All rights reserved.