Assalaamu alaykum. I was recently reading an article detailing how Muslims and non-Muslims should interact. The link to it is here: https://iloveimamrabbani.wordpress.com/2013/03/23/how-should-muslims-behave-and-interact-with-kafirs/
The article says that it is Kufr (disbelief) and apostasy to honor a disbeliever in the same way that you would honor your fellow Muslims. My family consists of disbelievers, but if I honor them in the same way as a Muslim or more than that, have I disbelieved then? Thank you.

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.

First of all, it should be noted that Islam set strict limits in regard to declaring a Muslim to be a Kaafir (disbeliever) or apostate; not any statement or action renders a Muslim a disbeliever.

Regarding the statement or action that is Kufr, there is a difference between the statement and its speaker and between Kufr and the Kaafir. There are some Islamic conditions that must be met in this regard, which we have already highlighted in fatwas 8106 and 87963.

Secondly: the Sharia permits being kind to disbelievers. Allah says (what means): {Allah does not forbid you from those who do not fight you because of religion and do not expel you from your homes – from being righteous toward them and acting justly toward them. Indeed, Allah loves those who act justly.} [Quran 60:8]

Moreover, Asmaa' bint Abi Bakr, may Allah be pleased with her, said, “My mother came to visit me while she was an idolater at the time of the Prophet so I asked him, 'My mother has come desiring my kind treatment. Shall I keep ties with her?' He said, 'Yes, be dutiful to your mother.'” [Al-Bukhari and Muslim]

For more benefit, please refer to fatwas 254551 and 92413, which explain that non-Muslim parents have the right that their children treat them kindly and be dutiful towards them. We are not aware of any evidence that limits this kindness with certain limits. All this applies to the apparent treatment, without loving them in the heart or being an ally to them.

Thirdly: there are Islamic texts that forbid loving disbelievers and being an ally to them. Allah says (what means): {You will not find a people who believe in Allah and the Last Day having affection for those who oppose Allah and His Messenger, even if they were their fathers or their sons or their brothers or their kindred. Those – He has decreed within their hearts faith and supported them with spirit from Him. And We will admit them to gardens beneath which rivers flow, wherein they abide eternally. Allah is pleased with them, and they are pleased with Him – those are the party of Allah. Unquestionably, the party of Allah – they are the successful.} [Quran 58:22]

Fourthly; having affection for non-Muslims and being an ally to them does not entail judging a Muslim to be a disbeliever in all cases. Shaykh Ibn Taymiyah when speaking about the story of Haatib, may Allah be pleased with him, said:

“Since it is confirmed that what Haatib did is not an act of apostasy – and this is something agreed upon by the consensus of the scholars – despite the fact that if his message had reached the polytheists of Makkah, then Quraysh would have prepared themselves for the war, while the Prophet intended to keep the matter of fighting them secret, and what Haatib did was a great help for the disbelievers in their war against the Muslims in one of the most decisive battles between Islam and disbelief – if this is proven, it becomes known that help does not constitute Kufr unless the incentive for doing it is the love for the disbelievers and the wish that they would achieve victory over the Muslims.” 

Based on the above, there are details about this affection. It is based on these details that the matter should be understood.

Allah knows best.