When I was reading the question, I had a flash of insight into what I presume the question the OP is asking: how do we maintain "integrity" of DNA when we get a set of DNA from mother, and the other set from father (ignoring mitochondrial DNA and other neat things). I would assume this is the question due to the key word reproduction, but anyway,I am here to provide an answer.
As an answer:
I believe the OP has a misconception. DNA of the parents do not pair up in the progeny. Rather, we have 23 pairs of chromosomes, or 46 total chromosomes. What does this mean? The set from the mother and the father do not come together, like a zipper, and have certain bases that just happen to be different (due to single nucleotide polymorphisms and whatnot). Instead, there are two sets of DNA, each with a double helix.
I think this may be what AliceD is also conveying, but I wished to add some more points such as bringing to numbers to help clarify. If I misunderstood, please clarify!