Surat Al-Mai'dah, Verses 72-75 say:
[5:72] They have certainly disbelieved who say, " Allah is the Messiah, the son of Mary" while the Messiah has said, "O Children of Israel, worship Allah , my Lord and your Lord." Indeed, he who associates others with Allah - Allah has forbidden him Paradise, and his refuge is the Fire. And there are not for the wrongdoers any helpers.
[5:73] They have certainly disbelieved who say, " Allah is the third of three." And there is no god except one God. And if they do not desist from what they are saying, there will surely afflict the disbelievers among them a painful punishment.
[5:74] So will they not repent to Allah and seek His forgiveness? And Allah is Forgiving and Merciful.
[5:75] The Messiah, son of Mary, was not but a messenger; [other] messengers have passed on before him. And his mother was a supporter of truth. They both used to eat food. Look how We make clear to them the signs; then look how they are deluded."
The Islamic concept of God does not subscribe to the Trinity concept, but to the absolute oneness of God. As such, the Qur'an does not teach a certain Trinity — the phrase "The Father, the Son and The Holy Spirit" is not mentioned anywhere in the Qur'an.
However, it is common knowledge that the Christian concept of Trinity involves The Father, The Son and The Holy Spirit. Therefore, the "third of three" clearly references to the Christian concept of the Trinity and not Joseph, Mary and Jesus.