What is the role of a Muslim stepfather towards his non-Muslim stepdaughter, and is he responsible for her upbringing and education?

The child follows the better of their parents in religion. Therefore, your daughter is a Muslim, and you are responsible for her custody and upbringing without interference from the disbelieving father. Her stepfather (your husband) is forbidden to marry her because he has consummated marriage with her mother. He is not obligated to raise her, but it is recommended that he care for her and earn reward, following the example of the Prophet, peace be upon him, in raising his wives' children. He should win her heart with good treatment, and you have a role in strengthening the relationship between them.