This paper presents a study of the magnetoresistance (MR) in the layered magnetic structure (NiFeCo/Cu). The effect of the magnetic (m) and non magnetic (nm) layer thickness (t_m , t_nm) and the composition of the magnetic layer has been discussed in the framework of the Johnson-Camley semiclassical approach, which is based on the Boltzmann transport equation. Our results are compared with the experiments and seem to show good agreement. Indeed, three main features of the MR are reproduced: (i) Presence of MR peak at t_m^max which vary with the magnetic layer composition, (ii) A MR decrease with non magnetic layer thickness t_nm, (iii) The increasing magnitude of MR ratio with increasing Co content.