The faith of the parents of the Prophet (SAWA) is a matter in which the majority of Muslim scholars have agreed that the parents of the Prophet were from the best of the believers.
 
Many evidences from the Holy Qur'an and authentic Hadith prove their faith.
 
In the Holy Qur'an in Surah ash-Shu'ara (26), verse 219, Allah (SWT) says "you're running on the believers who prostrate to Allah (SWT)".
 
Ibn Abbas narrated from the Prophet (SAW) that he said "the meaning of this verse is that Allah transferred me from person to person, from Prophet to Prophet until I became Prophet".
 
This hadith is mentioned in:
·        Majma al-Zawa'id by Al-Haythami (vol 7, page 86)
·        Musnad al-Bazzar
·        Al-Majma' by al-Tabarani
 
Al-Suyuti in his book of Tafseer known as al-Durr Al-Manthur (vol 4, page 238), narrated that the Prophet (SAW) said "Allah (SWT) transferred me from pious fathers to pious mothers, all purified and noble and made me always in the best parents best grandparents".
 
Al-Kattani in his book Nazm al-Mutanathir Min al-Hadith al-Mutawatir (vol 1, page 190) narrated the hadith from the Prophet (SAWA) that "all the fathers and grandfathers and mothers and grandmothers of the Prophet (SAWA) were with the pure tawheed".
 
Bajuri in his hashiya on Jawharat al-Tawhid mentioned that the narrations that the parents of the Prophet (SAW) were all best of believers are unanimous (tawatur).
 
Those who claimed that the parents of the Prophet (SAW) will be in hellfire are cursed. There is a narration in Sunni books which is in Mawahib al-Jalil (vol 6, page 386). The narration says that Abu Bakr ibn al-Arabi was asked by someone that a person had claimed "that the parents of the Prophet (SAW) will be in the hellfire - what do you say about him?" He said "he is cursed (mal'oon) because Allah mentions in the Holy Qur'an that those who hurt Allah (SWT) and the Prophet (SAW) are cursed in this world and the hereafer and they will be facing terrible and insulting punishment". Then he said "there is no hurting greater than claiming that his (SAW) parents are in the hellfire".
 
Al-Suyuti, the well known Sunni scholar, has written an entire book by the name of Al-ta'zim wa al-minna fi anna abaway an-nabi fi al-janna proving that the parents of the Prophet are in paradise. He mentioned in vol 1, page 25, that Jibra'il came to the Prophet (SAWA) and he told him "Allah is conveying salam to you and informing you that hellfire is forbidden on your fathers and your mothers and those who looked after you". "Your fathers" refers to Abdullah, "your mother" refers to Aamina and "those who looked after you" are Abu Talib and Faitma bint Asad.
 
The above quotations are from Sunni books only . 
As far as Shia faith, no doubt we (the followers of Ahlul Bayt) believe that the parents of the Prophet (SAW) are not only believers but also from the best of believers.
 
We read in the ziyaaraat of our infallible Imams that all the grandfathers and grandmothers were purified and the best of believers in Allah (SWT).
 
 
Wassalam.