You can read the whole series here.
Pilate. Matthew and Luke.
In Matthew, Pilate’s questions are essentially the same as in Mark. Matthew adds, “so the governor wonders greatly.” It’s a little more drama. But in the Barabbas narrative, Matthew has “while Pilate was seated on the judgement seat.” Only John and Matthew reference the judgement seat. And this is genuine Roman practice. The Tribunali, the Bema, judgement seat, it was a show of formal meaningful procedure. “While he was there his wife sent word to him saying have nothing to do with that righteous man, for I have suffered much over him today in a dream.” This is early in the morning, recall the cock crow. This is Matthew all over, the Gospel of dreams. Joseph the dream master who echoes the original Joseph the dream master. The Gentiles worship baby Jesus (Magi) while the Jews try to kill him, and Matthew has king of the Jews there too, and now there is this Gentile woman who wants to protect Jesus, has a dream, etc. There is this excellent parallel between beginning and end.
Now, when Pilate sees there is a riot starting over this, “he took water and washed his hands before the crowd saying, I am innocent of this man’s blood, see to it yourself. And all the people answered his blood [is] on us and on our children.” The innocent blood business is here again and it just means Pilate puts responsibility for the death of Jesus in the hands of the Sanhedrin, but the crowd takes responsibility: “on us and on our children.” The “on our children” bit is a legal thing that arises in the Law of Moses: the blood of the innocent is visited on subsequent generations (and you see some flavor of this in D&C 68).
One of the curious things about Mrs. Pilate’s dream: what about Peter’s rebuke: “get thee behind me Satan.” And yet God apparently gives the woman a dream so stirring that she tells her husband not to get involved (something that would remove death as an option for Jesus). Maybe Matthew doesn’t remove blame from Pilate here, but it’s a lesser blame, he ultimately issues the order for execution.
Luke has a much smoother report of the Roman trial. Luke is aware of Roman procedure and he places his Gospel and its continuation in Acts within the broader Roman world. Luke wants the death of Jesus to be a model for condemned Christians and his accounts of Roman trials in Acts and in the Gospel inform each other. His report of Paul’s trip to Jerusalem (Acts 22-23), and the accusations from the Sanhedrin about Paul to Roman authorities is very close to Jesus’ experience. The Roman governor sits in judgement of Paul. Since there is a Jewish king in Jerusalem at the time, Agrippa II, the governor invites Agrippa into the trial to hear the case. It’s the same pattern. Luke also has Pilate send Jesus to a Herod, the same Herod who beheaded John the Baptist. It’s almost word for word in many spots.
Herod is pleased that Pilate sent Jesus to him, and he becomes friendly with Pilate after this. It’s not a question of jurisdiction. The alleged crime occurs in Jerusalem, but Jesus is identified as being from Nazareth, so that Herod has a kind of acknowledged interest in the case. When Herod first heard about Jesus, he was worried, because there was a rumor that it John the Baptist come back from the dead. When Jesus is headed up to Jerusalem, the Pharisees warn him that Herod wants to kill him. Jesus said, “go and tell that fox that it’s not the time.” Then when Pilate sends Jesus to Herod, Luke writes:
“When Herod saw Jesus, he was very glad.”
Luke says Herod was hoping to see some sign done by Jesus. Some magical work.
But again, Herod asked questions, but Jesus made no answer. So he says nothing either to Pilate or Herod. Then Herod mocks Jesus and puts “gorgeous apparel” on him and sends him back to Pilate. Luke avoids any mockery by Romans, he puts it all on Herod and Herod’s soldiers.
Now there is something odd about this. Luke quotes Peter in Acts 4:25-7 citing a Psalm (2):
who by the mouth of our father David, thy servant, didst say by the Holy Spirit, ‘Why did the Gentiles rage, and the peoples imagine vain things? The kings of the earth set themselves in array, and the rulers were gathered together, against the Lord and against his Anointed’ — for truly in this city there were gathered together against thy holy servant Jesus, whom thou didst anoint, both Herod and Pontius Pilate, with the Gentiles and the peoples of Israel
There is Hebrew parallelism here, like so:
Why did the Gentiles rage || the peoples imagine vain things
The kings of the earth set themselves in array || and the rulers were gathered together
against the Lord || and against his Anointed
The parallel phrases identify the same thing. However, the Gospel writers had lost the knowledge of the technique and they saw the parallel phrases as separate items. They tear open the parallelism and then look to find each piece fulfilled separately. The classic example is when the Gospel speaks of Jesus entering Jerusalem on a donkey and the foal of an ass. He’s not riding both, it’s one animal. Luke separates “king and ruler” seeing Herod and Pilate in the the Psalm. But in doing this, he has Herod and Pilate against Jesus. Yet in the Gospel he has Herod and Pilate finding Jesus innocent. It’s as though there are two traditions at work, one where Herod is against Jesus, one, perhaps with Luke’s benevolent attention, where Herod is friendly to Jesus. Piling up witnesses of Jesus’ innocence is Luke’s work. Though Luke is the only witness to this interaction with Jesus, it was apparently a popular idea among early Christians and this Herod is prominent in second century Christian literature like the Gospel of Peter.
By Common Consent, a Mormon Blog 
That’s interesting about not knowing the poetic structure. I’d never noticed that.