This article presents a method to compute the response of a viscoelastic layered half-space to a moving load when interlayer slip is considered. The Navier equations of equilibrium are solved for each layer in the frequency domain. The solution in the spatial coordinate system is subsequently obtained by means of Fast Fourier Transform and quadrature rules applied to integrable singularities. Following the global solution technique, the developed method compiles all the interface and the boundary conditions within a global matrix and it solves a unique linear system per couple of wave numbers. This method proves to be effective and is validated in an elastic case by comparison with the ALIZE-LCPC software that implements the Burmister axisymmetric solution. The influence of the interface sliding condition on the response of a layered viscoelastic medium is studied through an application to pavement structures. In this application, the effect of the load speed on vertical and horizontal profiles of the longitudinal strain and the normal stress is analyzed. It is shown, inter alia, that the maximum extension in the medium is not systematically observed at the location of an interface and that, as expected, low speeds and interlayer slip are more damaging to the structure when either a strain or a stress criterion is considered.