The sudden change in drilling conditions taking place at an interface between two rock layers creates parasitic forces and moments at the bit, which locally perturb the borehole trajectory. This perturbation can be determined by coupling a bit/rock interaction law with a model for the bottom-hole assembly (BHA). In this paper a linear bit/rock interaction that accounts for the difference of rock properties across the interface is developed and coupled with a BHA model, simplified on account that the positions of the stabilizers are assumed fixed in position when computing the influence of the interface at the length scale of the bit. The BHA is then modeled by springs that prevent the bit from moving freely. The theoretical predictions for a cylindrically-shaped bit are consistent with experimental results reported in the literature. A preliminary study on the influence of the main parameters influencing the perturbation is also presented.