Are Catholics Christian?

 In fact, we are the only Christians, properly speaking. From the Catechism of St Pius X,

12 Q. The many societies of persons who are baptised but who do not acknowledge the Roman Pontiff as their Head do not, then, belong to the Church of Jesus Christ?
A. No, those who do not acknowledge the Roman Pontiff as their Head do not belong to the Church of Jesus Christ.

From Complete Christianity

By Shane Schaetzel 

Yes, Catholics are not only Christians, but we were the first Christians. The Roman Catholic Church is the oldest Christian Church founded by Jesus Christ in AD 33, and planted in Rome in about AD 42 [Irenaeus, Against Heresies, 3:1:1 (AD 180); Eusebius of Caesarea, The Chronicle (AD 303)], when Saint Peter established his Apostolic see in Rome after planting a church in Antioch [Clement of Rome, The First Epistle of Clement, 5 (AD 96); Irenaeus, Against Heresies, 3:1:1 (AD 180); Eusebius, Church History, 2:14,5 (AD 325)]. Peter was later crucified in Rome, upside down, in the year AD 67 [Gauss, fragment in Eusebius’ Church History, 2:25 (AD 198); Tertian, Against Marcion, 4:5 (AD 210); Tertullian, Scorpiace,15:3 (AD 212); Peter of Alexandria, The Canonical Epistle, Canon 9 (AD 306); Cyril of Jerusalem, Catechetical Lectures, 6:14-15 (AD 350)]. His direct successors became the popes.

Do Catholics believe in Jesus Christ?

Yes, of course we believe in Jesus Christ. We believe he is God the Son – the Second Person of the Holy Trinity (Father, Son and Holy Spirit) – made flesh and blood, taking on a fully human form, and becoming fully man in every way, yet retaining his full divinity [Catechism of the Catholic Church, paragraphs 464 – 470, 480 – 482]. We believe in his life, virgin birth, miracles, ministry, suffering, death and resurrection. We also believe he is currently reigning as the King of kings in Heaven, and he will one day return to judge the living and the dead [Catechism of the Catholic Church; pages 56 – 57].

What do Catholics mean by the Holy Trinity?

We believe in ONE God, who is eternally existent in three divine Persons: Father, Son and Holy Spirit [Catechism of the Catholic Church, paragraphs 232, 234, 237, 261 & 266]. This is the teaching of the Holy Scriptures [Matthew 3:16-17; Matthew 28:19; John 1:1; John 8:59-59; John 10:30-33; John 14:26; John 15:26; John 20:28; 2nd Corinthians 13:14; Galatians 4:4-6; Titus 2:13] and the early Church. The first Christians gave their lives for this faith. As Justin Martyr wrote in AD 155: “Our teacher of these things is Jesus Christ, who also was born for this purpose, and was crucified under Pontius Pilate, procurator of Judaea, in the times of Tiberius Caesar; and that we reasonably worship Him, having learned that He is the Son of the true God Himself, and holding Him in the second place, and the prophetic Spirit in the third, we will prove.” – (Justin Martyr, First Apology 13)

The doctrine of the Trinity was taught from the earliest days of the Church, and it’s helpful to remember that the people who gave their lives as martyrs in the Roman circuses (made into human torches and lion food) died believing that Jesus Christ is God, and that he is the second Person of the Holy Trinity. The name “Trinity” was used as early as the third century to briefly describe the triune nature of God. The doctrine was finally defined dogmatically in the early fourth century at the Council of Nicea in response to the Arian heresy. In the early fourth century, a rogue priest named Arius introduced the teaching that Jesus Christ is not divine and that God is not a Trinity. This caused such a great disturbance in the early Church that an ecumenical council was called in the City of Nicea (located in Asia Minor) in which all of the bishops were summoned to investigate this matter. They condemned the Arian heresy, affirmed the Trinity as the universal faith taught by the Apostles, formulated the Nicene Creed, and ordered the compilation of a universal New Testament to combat this heresy. Thus, the Catholic Christian faith was dogmatically defined as those Christians who maintained belief in the Trinity, as opposed to those who followed Arius in denying the Trinity.

The doctrine of the Trinity is universally accepted by all Christian churches that broke with the Catholic Church in the sixteenth century and thereafter. It is taught by all Christian churches connected to the Catholic Church through history and baptism. It is the universal doctrine of all Protestant denominations: Lutheran, Anglican, Methodist, Reformed, Presbyterian, Baptist, Pentecostal, etc. Evangelicals are staunchly Trinitarian in their belief about God. Christianity has always been defined as a Trinitarian faith, meaning the belief in ONE God in three equally divine Persons. There are of course some churches that no longer teach the Trinity. These churches are no longer connected to the Catholic Church, neither through history nor baptism. For that matter, they are no longer connected to Protestantism or Evangelicalism, and most of them have no problem telling you that. 

The above paragraphs are taken from the book Are Catholics Christian? A Guide to Evangelical Questions about the Catholic Church, written by Shane Schaetzel. The book is highly recommended by priests and catechists alike. The Foreword is by Fr. Chori Seraiah, of the Personal Ordinariate of the Chair of St. Peter.