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?

Firstly: 

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)’”

[al-Maa’idah 5:73] 

“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)’”

[al-Maa’idah 5:116]. 

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 

Secondly: 

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”

[an-Nisa’ 4:11]. 

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.