Because Birdy's unit is a flex unit, they're passed around from officer to officer, each one giving them new orders. Here are the officers who make an appearance beyond just a name-drop:
Colonel Armand Rose is Sessions' boss. The unit doesn't see him much, but he does give them a pep talk before he sends them to As Sayliyah for a briefing. It's a place for rest, but that only makes everyone nervous.
Lieutenant Maire is a man from the 3rd Battalion who travels to Ba'qubah with the First Squad and medical to be their security. When they get there, though, Lieutenant Maire has a fight with Miller about whether to treat Iraqi children who shot at Americans. He doesn't think it's such a good idea. He loses the argument, though, and doesn't leave when Miller tells him he can.
Lieutenant Davis is from the Special Ops, Intelligence unit, and travels with Birdy's unit to see if there are hidden detonators in a Baghdad home. Davis explains the mission and translates to the Iraqi homeowners when they get there. He's polite, and offers to repay them for breaking down their door, before Marla finds detonators. He gets pretty freaked out before taking the men away.
Major Scott is a PSYOP official who tries to make an alliance with a tribal leader named Hamid. He's not too good at small talk.
Colonel Roberts meets Birdy's squad on their final mission, in a marshy area near Iran. He's the guy who explains that they have the kidnapped children, and that Birdy's squad's job is to lie to the tribal leader and say they'll negotiate for them in exchange for detonators. Nobody trusts him, not even Coles.
When the mission's is over, Roberts says a flippant sorry for Jonesy's death, but can't contain his happiness that the mission was a success.