Half-Elves are the product of humans and elves getting it on. As Elves and Dwarves are descended from humans, but via different means, they cannot blend among themselves. Thus far, only goblins seem to have that ability, with horrifying results.
Half-Dwarves are also called Gnomes. They are the product of a dwarf and human getting it on, which produces a slimmer, more intellectually sharper but less physically durable person.