Why does Alton Brown call for three types of milks in a recipe?
The main purpose of the one part of Half-and-Half is to aid in homogenization of the one part of milk and one part heavy cream.

Per this article (toward the end):


  Half and half is also a good solution for desserts that call for equal parts milk and cream, but have a tendency to separate. The fat has been homogenized in the half-and-half, so using it in desserts like panna cotta will deliver a smoother, more consistent result. 


The half-and-half also enhances desired texture/mouth feel properties.