Dust is a crucial component of the interstellar medium of galaxies. The presence of dust strongly affects the light produced by stars within a galaxy. As these photons are our main information vector to explore the stellar mass assembly and therefore understand a galaxy's evolution, modeling the luminous properties of galaxies and taking into account the impact of the dust is a fundamental challenge for semi-analytical models. We present the complete prescription of dust attenuation implemented in the new semi-analytical model (SAM): G.A.S. . This model is based on a two-phase medium originating from a physically motivated turbulent model of gas structuring (G.A.S. I paper). Dust impact is treated by taking into account three dust components: Polycyclic Aromatic Hydrocarbons, Very Small Grains, and Big Grains. All three components evolve in both a diffuse and a fragmented/dense gas phase. Each phase has its own stars, dust content and geometry. Dust content evolves according to the metallicity of it associated phase. The G.A.S. model is used to predict both the UV and the IR luminosity functions from z=9.0 to z=0.1. Our two-phase ISM prescription catches very well the evolution of UV and IR luminosity functions. We note a small overproduction of the IR luminosity at low redshift (z<0.5). We also focus on the Infrared-Excess (IRX) and explore its dependency with the stellar mass, UV slope, stellar age, metallicity and slope of the attenuation curves. Our model predicts large scatters for relations based on IRX, especially for the IRX- relation. Our analysis reveals that the slope of the attenuation curve is more driven by absolute attenuation in the FUV band than by disk inclination.We confirm that the age of the stellar population and the slope of the attenuation curve can both shift galaxies below the fiducial star-birth relation in the IRX- diagram. Main results presented in this paper (e.g. luminosity functions) and in the two other associated G.A.S. papers are stored and available in the GALAKSIENN library through the ZENODO platform.