From what I’ve learned, the Romans were very particular about language, and that the only officially approved languages for use in the Roman army were Latin and Greek. They also tended to station troops many hundreds of miles away from their homelands.
So for Romans stationed in Judaea in the First Century, would they have conversed with the local populace in Latin or Greek? I assume Aramaic would have been off-the-table for Centurions and Governors.
I’m mainly thinking of conversations such as those recorded in the New Testament. Many Jews were Hellenized, and therefore knew some Greek. So would that have made it more likely that Jews such as Jesus, Herod or the Sanhedrin would have conversed with the Romans in Greek?
I addressed a similar question here. The TL;DR as it pertains to your question is that Roman soldiers spoke ALL KINDS of languages. In the east, garrisoned units tended to be made up of mostly locals, or people from relatively nearby, so in Syria, Judea, and surrounding regions you would have heard a lot of Aramaic dialects and Greek. The general local populace would have spoken Aramaic and possibly Greek, but almost certainly not Latin in the first century. Legions were more multiethnic, but also didn't arrive in Judea until 66, so they wouldn't have had (as many?) locals in this period (but still had a lot of Aramaic speakers). Within legions more Latin knowledge was necessary to communicate with higher-ups, but if you were low enough rank it might not have mattered.
I'm not sure where you heard that Roman armies forbid languages other than Latin or Greek--that's not something I've encountered, and it wouldn't have been practical. At most, Greek would be adopted as a common language to facilitate multiethnic communication (in the east--I don't know the situation in Gaul and Britain), and, like I said, you might need Latin to communicate with officers from Rome and Italy.
You might be interested in some earlier answers on this topic. They would likely have conversed in Greek.
A specific biblical example has been discussed by u/jimros in this thread and here by a deleted user here. More generally the question of the Greek language has been written about by u/toldinstone (here), u/Misticsan (here), and most recently by u/LegalAction (here)