Snapshot multispectral cameras that are equipped with filter arrays acquire a raw image that represents the radiance of a scene over the electromagnetic spectrum at video rate. These cameras require a demosaicing procedure to estimate a multispectral image with full spatio-spectral definition. Such a procedure is based on spectral correlation properties that are sensitive to illumination. In this paper, we first highlight the influence of illumination on demosaicing performances. Then we propose camera-, illumination-, and raw image-based normalisations that make demosaicing robust to illumination. Experimental results on state-of-the-art demosaicing algorithms show that such normalisations improve the quality of multispectral images estimated from raw images acquired under various illuminations.