Joe inherited half his DNA from me and half from Kate. However, the DNA we provided to him was a shuffled up version from both our parents. Below is a painting of all 23 pairs of chromosomes, which show which parts of Joe's DNA came from each grandparent.
In each pair of lines below, the top line came from me, the bottom line from Kate and the colours show which grandparent specifically contributed it.
We could go further with this painting... on chromosome 1, I painted over part of the DNA from Kate's Dad with segments I know came from his mother, Rosey. How do I know it's hers? Because Bill shares that DNA with relatives on his maternal line.
So who's responsible for Joe's brown eyes? The OCA2 gene provides instructions for making a protein located in melanocyotes that can affect your skin, hair and eye color. That gene happens to be found a segment of chromosome 15 that was contributed by both our mothers.
Of course, scientists know of at least another dozen genes that influence those traits so it's not really that simple, not even accounting for non-coding DNA and epigenetics, which can switch genes off. Still, one day we may be able to figure out that Joe inherited his chin from his 3x great grandmother.