Is the husband responsible for teaching his wife religion?

Yes, the husband is responsible for ensuring that his wife and family know the basics of religion and fulfil their obligations.
Allah commands the believers to protect themselves and their families from the Fire, and tells the family to establish prayer. If the husband cannot teach her himself, he must give his wife the room and means to learn, such as classes on personal religious obligation (fardu ain). Teaching must be done with wisdom, not coercion or humiliation. See Rights of husband & wife.