The Word House (Ahlul-Bayt) in Holy Quran
House of Abraham (AS)
Quran testifies that Sarah, the wife of Prophet Abraham (AS), was blessed by angels and was given the glad tiding that she will give birth to two prophets of God: 11:71
And his wife, standing by, laughed when We gave her good tidings (of the birth) of Isaac, and, after Isaac, of Jacob. 11:72
She said: "Alas for me! Shall I bear a child when I am an old woman and my husband now is an old man? That would indeed be a strange thing!" 11:73
The (angles) said: Do You wonder at Allah's decree? The grace of Allah and His blessings be upon you, O People of the House! He is indeed worthy of all praise full of all glory!"
Since in the mercy and the bounty of God offered in the above verse to the People of the House of Abraham, it has been a tendency of some Sunni commentators and their anxiety to find some argument for their counting the wives of the Holy Prophet (PBUH&HF) in the terms Ahlul-Bayt. They argue that since Sarah the wife of Abraham is included in the term Ahlul-Bayt mentioned in the above verse, then all the wives of the Prophet (PBUH&HF) are included in the verse 33:33 relating to the purity and the excellence of the Ahlul-Bayt of Prophet Muhammad.
However, these commentators intentionally or otherwise ignore the significance of the address by the Angels. If Sarah, the wife of Abraham, is included in the term Ahlul-Bayt used in the above verse, it is not because she was the wife of Abraham, but because she was going to be the MOTHER of two prophets (Isaac and Jacob). She was mentioned by angles in the above verse as a member of Ahlul-Bayt, AFTER she RECEIVED the glad tiding that she is pregnant of Prophet Isaac (AS).
The matrimonial relation between and a man and a woman is only circumstantial and can be given up at any moment. She could never be a permanent partner to any husband to be included in the heavenly address who are endowed with the unique and heavenly excellence UNLESS she brings a son who becomes a Prophet or an Imam. Thus if we consider Sarah as a member of the House, it would be only because she would be the mother of Isaac, and not being the wife of Abraham. The verses 11:71-73 quoted above show that Sarah was called among Ahlul-Bayt after she got to know that she is having Isaac (AS).
House of Imran (AS)
Likewise, Quran mentions the mother of Moses among the Ahlul-Bayt of Imran. Again, as we can see in the following verses, the emphasis here is the MOTHER of Moses and not the wife of Imran: 28:12
And We ordained that he refuse to seek any foster mother before so she said: Shall I point out to you a household who will take care of him for you, and will be kind to him? 28:13
So We restored him to his mother that she might be comforted and not grieve, and that she might know that the promise of Allah is true. But most of them know not.
The mother of Moses is termed as Ahlul-Bayt, not for being the wife of Imran, but for being the mother of Moses, otherwise the wives who are subject to divorce and being substituted with women better than them (Quran 66:5) can't be considered as Ahlul-Bayt as pointed out by Zaid Ibn Arqam as well. This is illustrated with the wife of Noah and Lot, though they were the wives of such great servants of God, they were not considered Ahlul- Bayt. They perished along with the rest of community.
Let's remember what Zaid Ibn Arqam said: "Ahlul-Bayt (household) of the Prophet are his lineage and his descendants (those who come from his blood) for whom the acceptance of charity (Zakat) is prohibited."
The wife of Imran was in the lineage of the Moses, so was the wife of Abraham who was in the lineage of Isaac and Jacob. Similarly, if Fatimah (AS) is among the Ahlul-Bayt Prophet of Islam, it is because not only she was the daughter of the Prophet (PBUH&HF), but also she was the mother of two Imams.
House of Noah (AS)
And Noah Cried unto his Lord and said: "My Lord! Verily my son is of my family; and verily Your promise is true, and You are the most just of the judges."
He (Allah) said: "O Noah! Verily he is not of your family; Verily he is (of) conduct other than the righteous; Therefore do not ask what you have no knowledge about; Verily I advice you not to be of the ignorant ones." (Quran 11:45-46)
Abul Ala Maududi wrote in his commentary of the above verse that: "If a part of the body of a person becomes rotten and the surgeon decides to cut it off, he will not comply with the request of the patient, who says 'Do not cut because it is a part of my body'. The surgeon will reply, 'It is no longer a part of your body because it is rotten.' Likewise when a righteous father is told that his son is a worthless act, it means to imply that the efforts that you made to bring him up as a good son have gone waste for the work is spoilt and ended in utter failure."
Sunni reference: Commentary of Quran by Abul Ala Maududi (published by the Islamic Publications (Pvt) Limited), p367, under verse 11:45-46 Prophet Noah (AS) was pleading for his own son and the reply was that the lad was not worthy of being his son. It is made crystal clear by this verse that though one might be of the same blood and flesh, born through the same parents, but if the issue doesn't possess the good qualities of the parents then he or she is not of his parents' stock (as said in the second verse). Noah had three other sons, Aam, Sam and Yafas who were believers and who with their wives entered the Ark and were saved and Kanan was Noah's son by his OTHER wife who was a disbeliever and perished along with her son.
It can be concluded that if any one does not hold the goodness of the correct faith in Allah, be he the son of the Apostle, he is not to be of the stock of his parentage; His very birth through his own parents is denied to him, even the right to be on God's earth is withdrawn from him, and he is to be destroyed.
Thus, even one is to be the son of a prophet of Allah, the lack of righteousness gets him disowned from the progeny (Itrat) of the apostolic family. It is for this reason that the term Ahlul-Bayt is restricted to the deserving members of the House of the Prophet and doesn't cover all of those who are born from his blood. Ahlul-Bayt are only the individuals among Prophet's descendants who also had close affinity in character and utmost spiritual attainment with Prophet (PBUH&HF).