Just echoing:
My chain of command is as follows:
My techs, NCOs, MSAs -> ME -> Department of Surgery Chief (currently a civilian surgeon, formerly not a physician) -> DCCS (a physician who rarely practices) -> Hospital Commander (A nurse)
But wait, there's more!
That's the hospital's command structure, but you're also part of a regular military company. The chain of command is hazier there, but it is basically:
Me -> A bunch of civilians and maybe the company's first sergeant -> the company commander (a captain, MSC officer).
For your day-to-day work, the company has little involvement, and your chain is the hospital command. For all of your Army related training and requirements, the Company is your go to. They're calling you at 0300 for UAs, making sure you're present for PT, scheduling you for field training, AWT, and the M-9 range without asking you, that sort of thing.
Some stuff gets sign off from both sides. When I ask for leave, the DOS chief signs it, then it goes to the Company where the Company CO (a man two-grades lower than the DOS chief) signs off on it. MASP/ISP, etc. starts in the Company, and then ends up on the Hospital Commander's desk for final approval. ODE is the same way.
It is extremely convoluted and ridiculous, and it is a product of milmed being crammed into the same general format that every other military unit is assigned, while not being anything like any other military unit.
Often times, when I need something signed or when I have a question that cannot be answered via e-mail, I have to cancel at least a half day of clinic so that I can go back-and-forth between the company and the hospital to get signatures in person - because my time is considered the least important of all. For example: credentialing, MASP, ISP, ODE-related issues.