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?
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."
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.
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 Catechism of the Catholic Church 463 - 478. Read it, meditate and pray. Look up the references and citations in the scriptures. Ask the Holy Spirit for understanding along with piety and fear of the Lord. God has revealed his Word to us. But you can't read it once and understand. You have to read, pray and pursue it daily.