American Dad, Chinese Mom, Child Born in USA

I (dad) am a U.S. Born U.S. Citizen, my wife is a Chinese Citizen with no green card. If our child is born in America, citing several confusing Chinese Consulate websites, the child must apply for a Travel Document and is not eligible for a Chinese Visa. It seems like the determining factor is whether or not the Chinese parent has received a Green Card or Citizenship in America, and the American parent's nationality has no impact. Is this correct?