We report fluorescence microscopy studies of the electrophoresis of individual DNA molecules electrostatically adsorbed to a cationic supported lipid bilayer. Obstacles to uniform electrophoretic flow cause the 2-D chains to adopt hooked conformations similar to those previously observed in 3-D electrophoresis experiments. Analysis of the stretch-contraction dynamics allows for an estimate of the obstacle density in the bilayer. Increasing the electric field causes the DNA molecules to become more highly stretched and increases the electrophoretic mobility substantially. A comparison of the Rouse relaxation time of the polymers and the average time between chain-obstacle collisions reveals that a single-obstacle model is insufficient to describe the observed dynamics but the obstacles are not dense enough to use a reptative model. Analysis of the unhooking dynamics reveals an 80% increase in hydrodynamic drag as compared to free chains. Finally, we observe anomalous diffusion of the DNA chains, with a large increase in the diffusion coefficient after the repeated application of high electric fields. Implications of the flow obstacles in the engineering of separation applications are discussed.