The presence of sets of open fractures is common in most reservoirs, and they exert important controls on the reservoir permeability as fractures act as preferential pathways for fluid flow. Therefore, the correct characterization of fracture sets in fluid-saturated rocks is of great practical importance. In this context, the inversion of fracture characteristics from seismic data is promising since their signatures are sensitive to a wide range of pertinent fracture parameters, such as density, orientation and fluid infill. The most commonly used inversion schemes are based on the classical linear slip theory (LST), in which the effects of the fractures are represented by a real-valued diagonal excess compliance matrix. To account for the effects of wave-induced fluid pressure diffusion (FPD) between fractures and their embedding background, several authors have shown that this matrix should be complex-valued and frequency-dependent. However, these approaches neglect the effects of FPD on the coupling between orthogonal deformations of the rock. With this motivation, we considered a fracture model based on a sequence of alternating poroelastic layers of finite thickness representing the background and the fractures, and derived analytical expressions for the corresponding excess compliance matrix. We evaluated this matrix for a wide range of background parameters to quantify the magnitude of its coefficients not accounted for by the classical LST and to determine how they are affected by FPD. We estimated the relative errors in the computation of anisotropic seismic velocity and attenuation associated with the LST approach. Our analysis showed that, in some cases, considering the simplified excess compliance matrix may lead to an incorrect representation of the anisotropic response of the probed fractured rock.