Although sheep and goats seem similar and can be mated, they belong to different genera in the subfamily Caprinae of the family Bovidae.
Sheep belong to the genus Ovis and have 54 chromosomes, while goats belong to the genus Capra and have 60 chromosomes. The offspring of a sheep-goat pairing is generally stillborn.
Note, this is the natural form of what can also be created in the laboratory by combining the embryos of a goat and a sheep to create a chimera, which actually has four parents.
(Yep, the chimera can be fertile, but will breed true to goat or sheep, not both – which genes it passes on depends on whether its reproductive organs were goat or sheep).
Photo of Irish geep via International Business Times.
Via Wikipedia.