Answer
Herod was king over Galilee and Perea; Pilate was prefect over Judea and Samaria. Caesar was emperor over both these territories, so both Herod and Pilate were under his rule. Their positions seem to have been roughly equivalent in power, neither being under or over the other; they simply ruled different territory. This is why in Luke 23:6-7 Pilate sends Jesus to Herod when he hears that Jesus is from Galilee (there is some question about jurisdiction).
Answer by Ra McLaughlin
Ra McLaughlin is Vice President of Finance and Administration at Third Millennium Ministries.