The man is charged with manslaughter arising from the death of the girl on January 6, this year, and causing grievous bodily harm with reckless disregard arising out of an incident on December 19, last year.
The woman is charged with obstructing justice.
They are jointly charged with ill-treating the child.
Whether they get to keep their identities secret will be decided at a hearing in Gisborne District Court tomorrow.
The pair each made preliminary appearances in the court this afternoon. Judge Warren Cathcart remanded each of them further in custody overnight to appear again in the morning for legal arguments as to whether they should get interim name suppression.
The Gisborne Herald said it would oppose those applications.
Whether the pair are granted bail will also be discussed at tomorrow's hearing.