Islam orders the husband to treat his wife gently and to help her lead a good life irrespective of whether she is a Muslim or a non-Muslim. Pork is prohibited by the Hebrew Scriptures, and that is why the husband is required to convince his non-Muslim wife to choose another alternative for the sake of the family harmony, especially when there are children.
Dr. Jamal Badawi, professor at Saint Mary’s University in Halifax, Nova Scotia, Canada, and member of the European Council for Fatwa and Research, states the following: The Hebrew Scriptures make it unlawful to eat pork. Prophet Jesus (peace be upon him) never revoked that law. Actually he said, “I came not to destroy the law of Prophets.” However, it was Paul and Peter who made it lawful. But we are not required to interpret Christianity for its own adherents. 

If such couple have children, it may be preferable for the husband to appeal to her to choose another alternative for the sake of family harmony, because It is known that the pig is an unclean animal as both the Bible and the Qur’an state. It eats its own secretions. It is always carnivorous. There is much medical evidence which shows that it is harmful to health.