If he dies and leaves behind a father, mother, Christian wife, and brothers and sisters both full- and half-siblings, who among them inherits from him?
Your saying that your Christian wife is not a Muslim but she is a believer is a contradiction in terms and is not correct, because the one who is a believer is a Muslim. Perhaps you mean that she believes in the existence of God or that she believes in her religion. This and similar matters cannot be described as faith or Islam unless she believes in the Messenger of Allah Muhammad (blessings and peace of Allah be upon him) and she believes in all the Messengers of Allah.
The Christians are disbelievers and cannot be described as Muslims, let alone believers. Allah, may He be exalted, says (interpretation of the meaning):
“Surely, disbelievers are those who said: ‘Allah is the third of the three (in a Trinity)’”
“And (remember) when Allah will say (on the Day of Resurrection): ‘O ‘Eesa (Jesus), son of Maryam (Mary)! Did you say unto men: Worship me and my mother as two gods besides Allah?’ He will say: ‘Glory be to You! It was not for me to say what I had no right (to say)’”
In Saheeh Muslim (153) it is narrated from Abu Hurayrah (may Allah be pleased with him) from the Messenger of Allah (blessings and peace of Allah be upon him) that he said: “By the One in Whose hand is the soul of Muhammad, no one among this nation, Jew or Christian, hears of me then dies not believing in that with which I was sent, but he will be one of the people of the Fire.”
Shaykh al-Islam (Ibn Taymiyah – may Allah have mercy on him) said:
The Jews and Christians are disbelievers in a sense that is clear, and that is well established and well known in the religion of Islam.
End quote from Majmoo‘ al-Fataawa, 35/201
Inheritance refers to the living taking charge of the wealth of the deceased because of ties of blood or marriage.
The inheritance is not determined until after the death of the one from whom the wealth is inherited, after which we may see who among his heirs is entitled to take over his wealth that he left behind, according to the shares allocated by Allah.
We cannot at present specify who will inherit from you after you die, because we do not know who will die first; perhaps you will inherit from them or perhaps others will inherit from you.
But if we assume that you have left all of these people behind, then your inheritance goes to your father and your mother; and your wife and brothers and sisters, whether they are full- or half-siblings, do not get anything.
With regard to your wife, she does not inherit from you because she is a non-Muslim; a non-Muslim cannot inherit from a Muslim and a Muslim cannot inherit from a non-Muslim.
See the answer to question no. 26171
With regard to your brothers and sisters, none of them inherits because the father is present.
Allah, may He be exalted, says (interpretation of the meaning):
“if no children, and the parents are the (only) heirs, the mother has a third; if the deceased left brothers or (sisters), the mother has a sixth. (The distribution in all cases is) after the payment of legacies he may have bequeathed or debts”
Ibn Katheer (may Allah have mercy on him) said:
The third scenario with regard to parents is if parents are present along with siblings, whether they are from both parents or from the father or from the mother. They do not inherit anything if the father is present, but despite that they change the share of the mother from one third to one sixth. So if there are siblings, her share is changed to one sixth. If there is no heir apart from her and the father, the father gets the remainder (of the estate).
End quote from Tafseer Ibn Katheer, 2/199
Abu’l-Qaasim al-Khuraqi (may Allah have mercy on him) said: The brother and sister, whether they are full siblings or through the father only, do not inherit if there is a son or if there is a son’s son (grandson), no matter how far the line of descent extends, or if there is a father.
Ibn Qudaamah (may Allah have mercy on him) said: The scholars are unanimously agreed on this, praise be to Allah. That was mentioned by Ibn al-Mundhir and others.
End quote from al-Mughni, 6/163
Based on that, the mother inherits one sixth and all the rest goes to the father; none of the siblings or the wife inherits anything.
The siblings in this case block others and are blocked. They block the mother in the sense that they reduce her share from one third to one sixth, and they are blocked by the presence of the father, because he is closer to the deceased than them. The Prophet (blessings and peace of Allah be upon him) said: “Give the shares of inheritance to those who are entitled to them, and whatever is left goes to the closest male relative.”
Narrated by al-Bukhaari, 6732; Muslim, 1615
But you should understand that you have the right to bequeath part of your wealth to those who will not inherit from you, up to a limit of one third of what you leave behind. So if your wife will not inherit from you because she is Christian, and your siblings will not inherit from you, because they are blocked, then if you wish you may bequeath some of your wealth to whomever you want of these people, either to all of them or some of them, so long as what you bequeath is not more than one third of the entire estate that you leave behind. And if you do not make a bequest, there is no sin on you; if you make a bequest to some of them and not others, there is no sin on you either.
You have to honour your father and mother and treat them kindly, and uphold ties with all of your siblings, males and females, full siblings and otherwise, because that is what Allah has enjoined upon you.
And Allah knows best.