A Muslim woman does not have to observe hijab in front of a kaafir woman according to the more correct of the two scholarly opinions. Some scholars said that a Muslim woman should observe hijab in front of kaafir woman, quoting as evidence the verse in Soorah al-Noor where Allaah forbids the Muslim women to show their adornment to anyone except their husbands. Allaah says (interpretation of the meaning): 

“…and not to reveal their adornment except to their husbands, or their fathers, or their husband’s fathers, or their sons, or their husband’s sons, or their brothers or their brother’s sons, or their sister’s sons, or their women …”

[al-Noor 24:31]

Some scholars said that “their women” means believing women; if the women are kaafirs then the believing woman should not reveal her adornment to them. Others said that “their women” means the feminine gender, whether they are believing women or not. This is the more correct view. So the Muslim woman does not have to observe hijab in front of a kaafir woman, because it was proven that Jewish women in Madeenah at the time of the Prophet (peace and blessings of Allaah be upon him), and also idol-worshipping women, used to enter upon the wives of the Prophet (peace and blessings of Allaah be upon him), and there is no mention of them observing hijab in front of them. If that had been done by the wives of the Prophet (peace and blessings of Allaah be upon him) it would have been reported, because the Sahaabah did not omit anything, rather they transmitted everything, may Allaah be pleased with them. This is the preferred view and that which is most likely to be correct.