Abstract The implementation of an imperfect bond between the fibre and the matrix in the micromechanical model of cell assembly is achieved by two approaches. In the first one, a displacement jump at the fibre–matrix interface is introduced. The second approach replaces solely the fibre and the interphase by an equivalent medium. Our results show that the two approaches give the same estimation of effective elastic properties which describe the behaviour of the composite in its transverse plane. The combination of the tangential and normal interphase stiffness effect has been observed by loading a composite at a 45° off-axis. When the displacement discontinuity approach is used, the fibre–matrix interface has an important effect on failure modes generated in the composite. We have noticed that the loss of material strength is much greater as the fibre–matrix bond becomes poor.