Bismillahi Al-Rahmani Al-Rahim
Muslim Women With Non-Muslim Women
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
wa alaykum as-salam
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 Allah knows best.
[References: Nail Al-Ma'arib (2:511), Manar Al-Sabil (500), Mughni Al-Muhtaj (3:132)]
wa al-salamu `alaykum