We have calculated the electrical conductivity in the current-in-plane geometry of multilayered granular alloys composed of Co clusters embedded in Ag alternating with pure Ag layers. In particular, we have paid attention to the conductivity behavior as a function of Ag layer thickness, Co clusters' size, and degree of percolation. The electronic structure is self-consistently calculated within the unrestricted Hartree-Fock approximation using a parametrized tight binding Hamiltonian which includes a Hubbard-like term. The conductivity tensor is obtained by using the semiclassical Boltzmann equation in the anisotropic relaxation time approximation. We have used a s-d Mott-like scattering model for the electronic mean free path taking into account the Sondheimer's picture for electronic transport in thin films. We find that the experimental conductivity behavior at coalescence can be explained through the electronic band contribution. The conductivity behavior of continuous multilayers is already attained in the very early stage of percolation, as in the experiments.