David Feiss approached this problem in the series' opening title sequence: Mama had a chicken/Mama had a cow/Dad was proud/He didn't care how.
Sometimes opening credits are cumbersome vehicles for an origin story. The creators were faced with the question of whether and how to explain this scenario. There is one episode when cow is digging in the closet and pulls out what would be their upper halves and refers to them as their science projects.
Cow and Chicken are sister and brother, a cow and a chicken, but who have human parents whose faces are never seen in any episode (although there are references where you can see their shadows of their upper halves).
