When a clear layer is coated on a diffusing background, light is reflected multiple times within the transparent layer between the background and the air-layer interface. If the background is lit in one point, the angular distribution of the scattered light and Fresnel's angular reflectance of the interface induces a specific irradiance pattern on the diffuser: a ring-like halo. In the case where the background is not homogenously colored, e.g. a halftone print, the multiple reflection process induces multiple convolutions between the ring-like halo and the halftone pattern, which increases the probability for light to meet differently colored areas of the background and thus induces color change of the print. This phenomenon, recently studied in the case of a smooth layer surface (glossy finishing) is extended here to rough surface layer (matte finishing) in order to see the impact of the surface roughness on the ring-like halo, and thereby on the print color change. A microfacet-based bi-directional reflectance distribution function (BRDF) model is used to predict the irradiance pattern on the background, and physical experiments have been carried out for verification. They show that the irradiance pattern in the case of a rough surface is still a ring-like halo, and that the print color change is similar to the one observed with a smooth interface by discarding the in-surface reflections which can induce additional color change.