Highly non-coplanar extrasolar systems (e.g. Upsilon Andromedae) and unexpected spin-orbit misalignment of some exoplanets have been discovered. In Libert and Tsiganis (2011), a significant increase of the mutual inclination of some multi-planet systems has been observed during the type II migration, as a result of planet-planet scattering and/or resonant interactions between the planets. Here we investigate the effect of the inclination damping due to planet-disk interactions on the previous results, for a variety of planetary systems with different initial configurations and mass ratios. Using the damping formulae for eccentricity and inclination provided by the numerical hydrodynamical simulations of Bitsch et al. (2013), we examine their impact on the possible multiple resonances between the planets and how the growth in eccentricity and inclination is affected.