The holy spirit is gabrial (in arabic - Jibreel). The christians are the people of the book because it (gosipel) was revealed by Allah to Jesus but it was distorted by men through the passage of time. But there is still some essence of what Allah had originally revealed.
Now obviously you can't abide by a religion that has been distorted by man, so Allah sent His final Prophet to confirm what came before it (i.e. in the Torah and Gosipel) in the Qur'an and completed His favor upon mankind. Muhammad (saw) was sent to the whole world whereas Jesus and all other Prophets and Messengers were sent to a particular people.
To prove that there is still some truth in the bible can be proven by the words of Jesus, the Prophet of Allah, himself.
In the Gospel of John chapter 16 verse 7:
"Nevertheless I tell you the truth; it is expedient for you that I go away: for if I go not away, the Comforter will not come unto you; but if I depart, I will send him unto you".
And in Gospel of John chapter 16 verse 12-14:
"I have yet many things to say unto you, but ye cannot bear them now. Howbeit when he, the Spirit of truth is come, he will guide you unto all truth: for he shall not speak of himself; but whatsoever he shall hear, that shall he speak: and he will shew you things to come. He shall glorify me".
This is what is said in your books and the 'Comforter' is Muhammad, hence why Allah says in the Qur'an about the Prophet who is mentioned in the scriptures of the Jews and Christians.
Allah says in the Qur'an:
"Those who follow the messenger, the unlettered Prophet, whom they find mentioned in their own (scriptures),- in the law and the Gospel;- for he commands them what is just and forbids them what is evil; he allows them as lawful what is good (and pure) and prohibits them from what is bad (and impure); He releases them from their heavy burdens and from the yokes that are upon them. So it is those who believe in him, honour him, help him, and follow the light which is sent down with him,- it is they who will prosper."
[Surah Al Araf (The Heights) 7:157]
This is clearly talking about Prophet Muhammad, and the message that Islam convays is the same message that was convayed by Jesus, Moses and all other Prophets and Messengers.