The diffusion law of DMPC and DPPC in Supported Lipid Bilayers (SLB), on different substrates, has been investigated in details by Fluorescence Recovery After Patterned Photobleaching (FRAPP). Over micrometer length scales, we demonstrate the validity of a purely Brownian diffusive law both in the gel and the fluid phases of the lipids. Measuring the diffusion coefficient as a function of temperature, we characterize the gel-to-liquid phase transition of DMPC and DPPC. It is shown that, depending on the type of substrate and the method used for bilayer preparation, completely different behaviours can be observed. On glass substrates, using the Langmuir-Blodgett deposition technique, both leaflets of the bilayer have the same dynamics. On mica, the dynamics of the proximal leaflet is slower than the dynamics of the distal leaflet, although the transition temperature is the same for both layers. Preparing bilayers from vesicle fusion in same conditions leads to more random behaviours and shifted transition temperatures.