My girlfriend is Chinese, she is not born in a hospital so she doesn’t have her birth certificate, but a household registry, which is an official Chinese document.
According to the U.S. State Department’s reciprocity schedule for China, a notarial certificate (Gong Zheng Shu) issued by the Local Notary Public Office (Gong Zheng Chu) is required.
The notarial birth certificate typically contains a watermark, seal, and red stamp. It indicates the applicant’s name, gender, date of birth, ID number, place of birth, and both parents’ names. NOTE: Notarial birth certificates issued prior to 2012 may not list the ID number.
All notarial documents must have an English translation, and be attached with a certificate stating that the English translation is in conformity with the Chinese original.
So, the answer, in this case, is that your partner must obtain a notarial birth certificate.