We report on the wetting behavior of phospholipid membranes on solid surfaces immersed in aqueous solution. Using fluorescence microscopy, the spreading velocity of fluid bilayers advancing from a lipid source is investigated. The kinetic spreading coefficient was measured as a function of temperature for pure DMPC membranes and as a function of charge density and cholesterol content for binary membranes. A theoretical model for the membrane flow is presented, which takes into account the liquid crystalline bilayer architecture of the lipid membrane. The spreading power results from the membrane-solid VdW interaction and is dissipated in hydrodynamic shear flow as well as by inter-monolayer friction within the bilayer. The frictional drag causes a dynamic tension gradient in the spreading membrane, which is manifested by a single exponential decay of the fluorescence intensity profile along the spreading direction. Obstacles are shown to act as pinning centers deforming the advancing line interface. However, no depinning was observed, since the centers are circumflown without abrupt relaxation.