The surfaces of many objects in the Solar System comprise substantial quantities of water ice either in pure form or mixed with minerals and/or organic molecules. Sublimation is a process responsible for shaping and changing the reflectance properties of these objects. We present laboratory data on the evolution of the structure and the visible and near-infrared spectral reflectance of icy surfaces made of mixtures of water ice and non-volatile components (complex organic matter and silicates), as they undergo sublimation of the water ice under low temperature and pressure conditions (Poch et al., under review). We prepared icy surfaces which are potential analogues of ices found on comets, icy satellites or trans-neptunian objects (TNOs). The experiments were carried out in the SCITEAS simulation setup recently built as part of the Laboratory for Outflow Studies of Sublimating Materials (LOSSy) at the University of Bern (Pommerol et al., 2015a). As the water ice sublimated, we observed in situ the formation of a sublimation lag deposit, or sublimation mantle, made of the non-volatiles at the top of the samples. The texture (porosity, internal cohesiveness etc.), the activity (outbursts and ejection of mantle fragments) and the spectro-photometric properties of this mantle are found to differ strongly depending on the chemical nature of the non-volatiles, the size of their particles, the way they are mixed with the volatile component and the dust/ice mass ratio. The results also indicate how the band depths of the sub-surface water ice evolve during the build-up of the sublimation mantle. These data provide useful references for interpreting remote-sensing observations of Rosetta (see Pommerol et al., 2015b), and also New Horizons.