Bismillahi Al-Rahmani Al-Rahim

 Muslim Women With Non-Muslim Women
Q
 As-salam alaykum

[...]

Is it permissible for a Muslim woman to reveal her hair (or her neck
and lower arms - i.e. the 'lower' awrah) infront of a non-Muslim
woman?

Jazakum-Allah khairan

wa alaykum as-salam

 A
 wa `alaykum al-salam wa rahmatullahi wa barakatuhu, wa al-hamdu lillah.

[Note: Many thanks for Shaqur for finding the very big mistake.]

According to the madhhab, it is permissible for a women to show another woman--even a non-Muslim--anything other than the area between her navel and her knees.

A second opinion transmitted from Imam Ahmad (Allah be pleased with him) that a Muslima must cover in front of a non-Muslim woman the same as she must cover in front of men. This is also the opinion of the Shafi`is.

The reason for the difference of opinion goes back to understanding the phrase "nisa'ihinn" from Al-Nur (Qur'an 24:31):
And tell the believing women to lower their gaze and be modest, and to display of their adornment only that which is apparent, and to draw their veils over their bosoms, and not to reveal their adornment save to their own husbands or fathers or husbands' fathers, or their sons or their husbands' sons, or women, or their slaves, or male attendants who lack vigour, or children who know naught of women's nakedness. And let them not stamp their feet so as to reveal what they hide of their adornment. And turn unto Allah together, O believers, in order that ye may succeed." (Pickthall translation, p255)
T he phrase "nisa'ihinn" is composed of two words: the noun nisa' (women) and the pronoun hinn (their). Here there is a difference in understanding the scope of this pronoun: does it include women in general regardless of religion (which is the first opinion given), or is it restricted to Muslim women (the second opinion).

And Allah knows best.

[References: Nail Al-Ma'arib (2:511), Manar Al-Sabil (500), Mughni Al-Muhtaj (3:132)]

wa al-salamu `alaykum
--musa