This is the Nestorian heresy.
No, the Nestorian heresy is saying that Christ was two persons.
Nestorianism claimed that Jesus was host to two separate persons, that of the son of god and that of a mortal man. It was as such a direct response to Apollinarianism.
http://www.roman-empire.net/religion/heresy.html
Christ had two natures but was one Person.
Actually, some sources say Nestorianism claims two persons and some say two separate natures. I unfortunately don't know any Greek (yet), so I can't follow the controversy in original sources. But, using "natures," Nestorianism claimed that Mary was the mother only of the human nature and -- as a corollary -- that only the human nature suffered and died on the Cross, which leaves the theology of the Atonement rather in tatters . . .