I began watching the replay last night but fell asleep ... dang!
The Gospel was first proclaimed in Italian, and then a Greek deacon chanted a line, the Holy Father chanted something back (there was no interpretation of these chantings but it may have been a variation of the trisagion), and then the Gospel was chanted in Greek by the deacon. Simply beautiful!
The deacon is probably a priest and member of the Italo-Greek Catholic Church - one of only two Eastern Traditions that have never separated from the Magisterium. The other is the Maronite Church.
Benedict XVI has declared that he will actively pursue restoration with the Orthodox Churches. That would explain why you are seeing more Eastern Patriarchs and Bishops at the various papal services.
Towards the end of the JPII's funeral mass, overseen by then Joseph Cardinal Ratzinger, we were privileged to experience a Byzantine Service for the Dead.
The week following his funeral, the Church offered up the Novendiales Masses. On Thursday of that week, it was the Patriarch of the Maronite Church, Mar Nasrallah Cardinal Pierre Sfeir, who served as principal celebrant at the liturgy. Representatives from the other Eastern Catholic Churches were all in attendance as were many Latin Rite Cardinals.
Here's some interesting information regarding a beautiful monastery just south of Rome. To learn more, click on the link:
"In 1004 the Tuscolo hills welcomed a group of monks. An old holy man arriving, anxious to find a place to build a monastery to gather all his brothers. It was St. Nilus, born in Rossano, in Calabria, from a Greek family. At that time Calabria was under the Byzantine rule and was Greek in language, culture,and spiritual and liturgical tradition. Nilus had founded several monasteries in Calabria and in Campania. Though a humble saint, he was held in high esteem by Princes, Emperors and Popes. Having flown from place to place to avoid all honours, he finally wanted to reach Rome to end his days in peace."
S. Maria di Grottaferrata