We do not know of any Islamic rulings or etiquette that enjoins the woman to wear jijab even when she is on her own in the house or with her husband.
Although your husband’s gheerah (protective jealousy) is to be appreciated, what he is demanding comes under the heading of extreme strictness which is contrary to Islam and to sound human nature (fitrah). Allah, may He be exalted, has made sound hearts love adornment and beauty, and Allah has permitted a great deal of that, including a woman’s adorning herself and beautifying herself for her husband. This is something that makes the husband love his wife and creates a good relationship between them.
Al-Manaawi (may Allah have mercy on him) said:
As for putting on perfume and adorning oneself for one’s husband, it is required and recommended. Some of the scholars said: The wife’s adorning herself and putting on perfume for her husband are among the strongest causes of love and harmony between them and keeps dislike and resentment at bay, because the eye is the way to the heart, so if the eye sees something and likes it, it goes straight to the heart and thus love is generated. If it looks at something ugly or something that it does not like of clothing or garments, it will go to the heart and thus resentment and hatred will be generated. Hence the Arab women used to advise one another: Beware of letting your husband see you in a way that he does not like or smell something from you that he finds off-putting.
End quote from Fayd al-Qadeer, 3/190
If a woman wears hijab at home and with her husband, this will prevent her from a lot of adornment and beautification.
It should be said to the husband: Islam encourages the woman to adorn herself and beautify herself for her husband, and women are created with a natural inclination towards adornment and beauty, as Allah, may He be exalted, says (interpretation of the meaning):
“(Like they then for Allaah) a creature who is brought up in adornments (wearing silk and gold ornaments, i.e. women), and who in dispute cannot make herself clear?”
So do not put restrictions on something that Allah has made broad in scope. A woman’s wearing hijab in her husband’s house is not something that is indicative of higher levels of faith, it is not one of the things that bring barakah to the home, and it is not part of the etiquette that is encouraged in Islam.
The sign of faith is adhering to the laws of Allah; barakah is attained by following the commands of Islam and keeping away from dubious matters.
Enjoy what Allah has permitted to you and to her; ask her to adorn herself and beautify herself, and you will see that goodness and barakah are to be found in this, in sha Allah.
For more information, please see the answer to question no. 126454
And Allah knows best.