How to Deal With Non-Muslim Parents

How to Deal With Non-Muslim Parents

Wa `alaykum as-salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Thank you for your good question and your interest to know Islam's teachings towards your parents though they are non-Muslims.
Indeed, Islam gives a high priority to the relationship between children and parents by ordaining the children to obey their parents, including non-Muslim parents. Muslim children are ordained not only to obey and treat well their parents, but they are also prohibited to irk them with even a minor sound as a sign of irritation.
In one of these divine orders Allah Almighty says in the Qur'an, (And make yourself submissively gentle to them with compassion, and say: O my Lord! have compassion on them, as they brought me up (when I was) little.) (Al-Israa’ 17: 23)
The Sunnah also highly asserts this; `Abdullah ibn Mas`ud (may Allah be pleased with him) said, "I asked the Prophet (peace and blessings be upon him), "What is the best of deeds?" He said, "Prayers at their due time", I said, "What next?" He said, "Filial dutifulness, (i.e. dutifulness to parents)", I asked, "What next?" He said, "Jihad." (Al-Bukhari)
Responding to your question, Sheikh Gamal Qutb, the Ex-Head of the Fatwa Committee at Al-Azhar Ash-Shareef, stated,
Parents, whether Muslims or not, have the same rights upon their children including: respect, reverence, obedience, love, and spending if they are in need. Allah the Exalted ordained Muslim children to have the best behavior towards their parents even if they were non-Muslims. He Almighty says in the Qur'an, (And if they contend with you that you should associate with Me what you have no knowledge of, do not obey them, and keep company with them in this world kindly, and follow the way of him who turns to Me, then to Me is your return, then will I inform you of what you did.) (Luqman 31: 15)
It is clear in this verse that children have to keep the best relation to their parents (keep company with them in this world kindly), even if they are struggling to lead them astray. However, they must disobey them only when ordered to abandon their faith or to become pagans.
As for the Sunnah, Asma' bint Abi-Bakr (may Allah be pleased with her) said, "My mother (the divorcee of Abu-Bakr) came to visit me during the covenant between the Prophet and Quraysh. Then I asked the Prophet (peace and blessings be upon him) saying, "My mother came to me desirous, can I communicate with her?" He said, "Yes, make good your relation with your mother." (Al-Bukhari and Muslim)
Given the above, it becomes very clear that you should have the best treatment towards your parents even if they are non-Muslims, as the children owe them a great debt, (of course not a financial debt), and they have to repay some of these debts especially in their old age.
Allah Almighty knows best.