Praise be to Allah.
A sheep or ram for the udhiyah is only valid on behalf of one person, so it is not valid for two people to share in the sacrifice of a sheep, or of one seventh of a cow or camel. This sharing or partnership is not allowed.
The sharing or partnership that is allowed is sharing the reward, in the sense that a man offers a sacrifice and lets his family share in the reward, or a woman offers a sacrifice and lets her husband share in the reward. Please see the answers to questions no. 112264 and 36387.
Ibn al-Qayyim (may Allah have mercy on him) said: The teaching of the Prophet (blessings and peace of Allah be upon him) is that the sacrifice of a sheep is acceptable on behalf of a man and on behalf of the members of his household, even if they are many in number, as ‘Ataa’ ibn Yasaar said: I asked Abu Ayyoob al-Ansaari: How were the sacrifices (udhiyah) offered at the time of the Messenger of Allah (blessings and peace of Allah be upon him)? He said: A man would sacrifice a sheep on his own behalf and on behalf of the members of his household, and they would eat from it and give some of it away. At-Tirmidhi said: This is a saheeh hasan hadith. End quote from Zaad al-Ma‘aad (2/295).
Ibn Rushd said: The scholars are unanimously agreed that a ram is only acceptable on behalf of one person, apart from what Maalik narrated about it being acceptable for a man to sacrifice it on behalf of himself and on behalf of the members of his household, but not by way of sharing the cost; rather this applies if he buys it by himself. That is because of the report narrated from ‘Aa’ishah, according to which she said: We were at Mina and some beef was brought in to us. We said: What is this? They said: The Messenger of Allah (blessings and peace of Allah be upon him) has offered a sacrifice on behalf of his wives.
End quote from Bidaayat al-Mujtahid (2/196).
It says in Tuhfat al-Muhtaaj (9/349): A sheep or a goat is acceptable on behalf of one person only, according to scholarly consensus, and is not acceptable on behalf of more than that.
In fact, if the couple sacrifice two sheep, sharing the cost between them, that is not acceptable, because neither of them has sacrificed one entire sheep.
The hadith “O Allah, this is on behalf of Muhammad and the ummah of Muhammad” is to be understood as meaning that the reward is shared, which is permissible. Hence they said: One may let others share in the reward of his sacrifice (udhiyah)… End quote.
The wife may give some of her money to her husband so that he will be able to purchase an udhiyah and he will be the one to offer it, and he may let his family share in the reward.
Or vice versa, that he may give her money, so that the sacrifice is offered by her, and she lets her husband share in the reward. The reward is, in principle, for the one who offers the sacrifice; as for the other person (who is sharing in the reward), he is included as subordinate in this action.
If the wife shares the cost of the udhiyah with her husband, intending to help him to purchase it, because he does not have enough money, then there is nothing wrong with that.
Shaykh ‘Abd al-Kareem al-Khudayr (may Allah preserve him) was asked: What is the ruling on me sharing with my wife in the udhiyah? And what are the rulings connected to that?
He replied: If the head of the household offers the udhiyah, that sacrifice is sufficient on his own behalf and on behalf of the members of his household. So if the husband offers the udhiyah on his own behalf and on behalf of the members of his household, that is sufficient, and the wife does not have to offer a sacrifice on her own behalf.
That applies unless what is meant is that he pays half of the price and she pays the other half, so that they share in it on this basis. The basic principle is that the udhiyah is to be offered on behalf of the head of the household – the husband – and his wife and children are included with him.
But if that is by way of helping him, because he cannot afford the price of the udhiyah, and his wife wants to help him with the cost, then there is nothing wrong with that.
And Allah knows best.