The existence of an Inferno (Hell) is an element of the Christian tradition as is the belief in the Holy Trinity. This belief informs the very structure of the Inferno (there are nine circles and the narrative is divided in 33 cantos, plus an introductory canto to the entire Comedy). There are also important references to the Bible and Christian theology. Dante's interpretation of human history is always Christian in nature. This is what Auerbach calls "figural" or "typological" procedure. In this conception, historical events and characters dating back to before the advent of Christianity ultimately represent and pre-figure events and characters belonging to Christianity. For example, the Roman Empire of Augustus which had its official poet in Virgil is read by Dante as an image of God's Kingdom. This procedure was not invented by Dante, but is at the heart of Christianity itself and theologians have explained the relationship of the Old and New Testaments through this concept.
Yet, in Dante's Inferno, Greco-Roman traditions and beliefs are important too. The order of the sinners and the idea of evil are borrowed from Greek and Roman culture and are particularly indebted to Aristotle. In addition, Dante's conception of the universe is clearly derived from the Ptolemaic tradition with the Earth at the center. In this case, however, there is no contrast between the Greco-Roman and Christian traditions as the Church adopted the Ptolemaic model of the universe.
Finally, it shouldn't be surprising that the Inferno and the entire Commedia have both Greco-Roman and Christian elements. Dante's oeuvre was thought as a summa of all cultural traditions and philososphical beliefs that constituted Middle-Ages knowledge.