The surfaces of many objects in the Solar System comprise substantial quantities of water ice sometimes mixed with minerals and/or organic molecules. The sublimation of the ice changes the structural and optical properties of these objects. We present laboratory data on the evolution of the structure and the visible and near-infrared spectral reflectance of icy surface analogues of cometary ices, made of water ice, complex organic matter (tholins) and silicates, as they undergo sublimation under low temperature (<-70°C) and pressure (10-5 mbar) conditions inside the SCITEAS simulation chamber. As the water ice sublimated, we observed in situ the formation of a porous sublimation lag deposit, or sublimation mantle, at the top of the ice. This mantle is a network of filaments made of the non-volatile particles. Organics or phyllosilicates grains, able to interact via stronger inter-particulate forces than olivine grains, can form a foam-like structure having internal cohesiveness, holding olivine grains together. As this mantle builds-up, the band depths of the sub-surface water ice are attenuated until complete extinction under only few millimeters of mantle. Optically thick sublimation mantles are mainly featureless in the near infrared. The absorption bands of the minerals present in the mantle are weak, or even totally absent if minerals are mixed with organics which largely dominate the VIS-NIR reflectance spectrum. During sublimation, ejections of large fragments of mantle, triggered by overpressures, expose ice particles to the surface. The contrast of brightness between mantled and ice-exposed areas depends on the wavelength range and the dust/ice ratio considered. We describe how the chemical nature of the non-volatiles, the size of their particles, the way they are mixed with the ice and the dust/ice mass ratio influence the texture, activity and spectro-photometric properties of the sublimation mantles. These data provide useful references for interpreting remote-sensing observations of comets and also icy satellites or trans-neptunian objects.