Results. We describe the physical characteristics of the crystalline water ice present on the surface of Haumea for both regions, in and out of the DRS, and analyze the differences obtained for each individual spectrum. The presence of crystalline water ice is confirmed over more than half of the surface of Haumea. Our measurements of the average spectral slope (1 : 45 +/- 0 . 82% by 100 nm) confirm the redder characteristic of the spot region. Detailed analysis of the crystalline water-ice absorption bands do not show significant differences between the DRS and the remaining part of the surface. We also present the results of applying Hapke modeling to our data set. The best spectral fit is obtained with a mixture of crystalline water ice (grain sizes smaller than 60 mu m) with a few percent of amorphous carbon. Improvements to the fit are obtained by adding similar to 10% of amorphous water ice. Additionally, we used the IFU-reconstructed images to measure the relative astrometric position of the largest satellite Hi'iaka and determine its orbital elements. An orbital solution was computed with our genetic-based algorithm GENOID and our results are in full agreement with recent results.