Optical DNA mapping (ODM) allows visualization of long-range sequence information along single DNA molecules. The data can for example be used for detecting long range structural variations, for aiding DNA sequence assembly of complex genomes and for mapping epigenetic marks and DNA damage across the genome. ODM traditionally utilizes sequence specific marks based on nicking enzymes, combined with a DNA stain, YOYO-1, for detection of the DNA contour. Here we use a competitive binding approach, based on YOYO-1 and netropsin, which highlights the contour of the DNA molecules, while simultaneously creating a continuous sequence specific pattern, based on the AT/GC variation along the detected molecule. We demonstrate and validate competitive-binding-based ODM using bacterial artificial chromosomes (BACs) derived from the human genome and then turn to DNA extracted from white blood cells. We generalize our findings with in-silico simulations that show that we can map a vast majority of the human genome. Finally, we demonstrate the possibility of combining competitive binding with enzymatic labeling by mapping DNA damage sites induced by the cytotoxic drug etoposide to the human genome. Overall, we demonstrate that competitive-binding-based ODM has the potential to be used both as a standalone assay for studies of the human genome, as well as in combination with enzymatic approaches, some of which are already commercialized.