One question that has haunted the Catholic Church from the very beginning is about the way divine and human are related in the person of Jesus Christ. The differences in doctrines have lead to the creation of Assyrian Church of the East and Oriental Orthodox Church. The Council of Chalcedon in AD 451 has accepted Dyophysitism as the accepted Catholic doctrine. But is this the final stand made by the Catholic Church? Or did any post Chalcedonian councils further clarified this matter? This being such a sensitive topic could any one please explain the official Catholic position on the nature of Christ?
Modern Catholic christology describes a Hypostatic union.
Wikipedia discusses briefly how this is historically related to Dyophisitism:
Theodore of Mopsuestia [argued] that in Christ there were two natures (dyophysite) (human and divine) and two hypostases (in the sense of "essence" or "person") that co-existed. However in Theodore's time the word hypostasis could be used in a sense synonymous with ousia (which clearly means "essence" rather than "person") as it had been used by Origen and Tatian.
So the short answer to your question appears to be that, yes, this is still the view held by Catholicism, but it has been refined over the last 1500 years.
Yes, there were subsequent ecumenical councils that dealt with the matter. As explained in the Catechism of the Catholic Church, paragraph 468:
After the Council of Chalcedon, some made of Christ’s human nature a kind of personal subject. Against them, the fifth ecumenical council at Constantinople in 553 confessed that "there is but one hypostasis [or person], which is our Lord Jesus Christ, one of the Trinity." Thus everything in Christ’s human nature is to be attributed to his divine person as its proper subject, not only his miracles but also his sufferings and even his death: "He who was crucified in the flesh, our Lord Jesus Christ, is true God, Lord of glory, and one of the Holy Trinity."
The official Christological view of Catholic Church is dogmatized in her twenty one Ecumenical Councils. Council of Florence in relation to the eternal procession of the Holy Spirit from the Father through the Son is indispensable for Catholic. In those councils, the same Apostolic faith passed down from the Apostles are kept. That the whole and only person of Christ is the Logos, a divine person. Who has two natures: divine and human. This is why we Catholic call the virgin Mary, Theotokos (Greek for Mother of God). Because the one she gave birth is not merely a human nature but a divine person, the Logos. Nature can't be conceived but a person does. Because the Spirit proceeds from the Father through the Son, visible ecclesial communion with the Church of Rome is important. While regarding the relationship between Catholic with other separated brethren progress in ecumenical dialogues have been made significantly including the last meeting between Pope Francis and Patriarch Bartholomew of Constantinople to commemorate the mutual annulment of anathemas in 1054.
The Church's official view is that this sure is an important question, and you should probably go try and come closer to the truth of it through prayer, fasting, and participation in the Church. The most common verbalized approximation to an answer to this question is that Christ is both Fully God and Fully Man, but this, the Church confesses, is a poor shadow of a description of just one aspect of Christ's nature.
The titles of Christ give some insight into Christ's nature as well, and some of them, revealed in the scriptures, can be found here, though there are many, many others.
Even the nature of His name is the subject of prayer and theoria in the Church, as can be read about here.
In the end, as with nearly all great theological questions, the Church teaches that only theoria can profitably approach the answer, and thus everyone must come to learn the Truth themselves, through the development of their faith over the course of their lives. This question, a manifestation of the desire to know and understand the nature of Our Lord and Savior, Jesus, who is the Christ, and, indeed, the whole of the Trinity by extension (for how can one understand the Son unless he understands the Father? Everything the Son has is from the Father, and they are of one substance, inseparable) is regarded as perhaps the most important of the Mysteries:
The Mystery of Faith