Human blood platelets are non-nucleated fragments of megakaryocytes and of high importance for early hemostasis. To form a blood clot, platelets adhere to the blood vessel wall, spread and attract other platelets. Despite the importance for biomedicine, the exact mechanism of platelet spreading and adhesion to surfaces remains elusive. Here, we employ metal-induced energy transfer (MIET) imaging with a leaflet-specific fluorescent membrane probe to quantitatively determine, with nanometer resolution and in a time-resolved manner, the height profile of the basal and the apical platelet membrane above a rigid substrate during platelet spreading. We observe areas, where the platelet membrane approaches the substrate particularly closely and these areas are stable on a time scale of minutes. Time-resolved MIET measurements reveal distinct behaviors of the outermost rim and the central part of the platelets, respectively. Our findings quantify platelet adhesion and spreading and improve our understanding of early steps in blood clotting. Furthermore, the results of this study demonstrate the potential of MIET for simultaneous imaging of two close-by membranes and thus three-dimensional reconstruction of the cell shape.