How is a Muslim's child, born to a non-Muslim mother, buried if he dies?

A child is judged to be Muslim, following the religion of their Muslim father. It is obligatory to prepare their body, bury them in Muslim cemeteries, and treat them as Muslims. It is permissible to marry a chaste woman from the People of the Book with the permission of her guardian, the giving of the dowry, and the presence of witnesses.