The husband should tell his wife to wear hijab, even if she is Christian or Jewish, because the sin of her being uncovered and showing her adornment will be on him. The husband has the right to instruct his wife to do what she thinks it is permissible and he thinks is obligatory, and she has to obey him in that regard, as discussed previously in the answer to question no. 97125.
For more information please see also the answer to question no. 70177
The Standing Committee for Issuing Fatwas was asked:
In some countries it is rare for Muslim women to wear hijab. A man married a Muslim woman and she does not want to wear hijab. Should he divorce her or what should he do? Another Muslim married a kitaabi (Jewish or Christian) woman and she does not want to wear hijab either. What is the ruling?
The woman who refuses to cover herself in front of non-mahram men is regarded as disobedient to her husband and going against the laws of Allah. Her husband should advise her to wear proper shar‘i hijab, and if she does not respond then he should divorce her, whether she is Muslim or Jewish or Christian, so as to keep away from evil and protect the family from sin. And Allah is the source of strength. May Allah send blessings and peace upon our Prophet Muhammad and his Family and Companions.
End quote from Fataawa al-Lajnah, 17/108
Hijab is obligatory for Christian women, as it says in Didascalia Apostolorum (Teachings of the Apostles) which is regarded as the secondary book on religious law for Orthodox Christians. On p. 72 it says:
“Thou therefore that art a Christian, do not imitate such women; but if thou wouldst be a faithful woman, please thy husband only. And when thou walkest in the street, cover thy head with thy robe, that by reason of thy veil thy great beauty may be hidden. And adorn not thy natural face; but walk with downcast looks, being veiled.
[i. 9] And take heed that thou bathe not in a bath with men. For when there is a women's bath in the city or in the village, a believing woman may not bathe in a bath with men. For if thou coverest thy face from strange men with a veil of modesty, how then canst thou go in with strange men to a bath?”
End quote from Didascalia Apostolorum (Teachings of the Apostles), translated into Arabic by the Hegumen Marqus Dawood, Maktabat al-Mahabbah edn. (English translation by R. Hugh Connolly, Oxford: Clarendon Press, 1929).
So think about this command to observe hijab and this prohibition on displaying oneself and showing adornments to men. How many Christian women follow these teaching nowadays?!
And Allah knows best.