It's this bit that I found a bit misleading. It sounds as if the double helix is formed by the DNA from mom and pop forming a double helix structure between themselves. Which is of course not the case.
Two DNA Molecule
DNA is a very long molecule that consists of different building blocks. The order of the building blocks forms a certain code a cell takes instructions from to produce certain substances and start processes.
Two DNA molecules attach to each other and intertwine like an old-fashioned phone cord. DNA and certain proteins form the chromosomes.