A couple of things. Which branch? Are you talking the commissioning ceremony itself or the senior graduation dining out?
For our DS, (AFROTC) there were two functions. The dining out is a formal function. DS wore his Mess Dress (military tux). Parents wore dark suits and cocktail dresses. GFs wore gowns. There were Dad's in tuxes, but again they were wearing Mess Dress.
The official commissioning (pin on) occurred during the day for our DS. Bullet. Commissioned DS so he wore his service uniform. The rest of us wore Sunday best. Yes, I bought a specific dress for the commissioning, along with buying a dress for our DD. It is a once in a lifetime picture taking moment. I wore Navy Blue, our DD wore Lilly Pulitzer, and younger DS wore Navy slack with white shirt and a Navy tie.
I will say this, emotionally watching them receive their college diploma is one of the proudest moments a parent can have, but until you watch your child commission you cannot even fathom it. The college degree is nothing compared to the commissioning.
~~~~ DS commissioned from UMDCP. They do it at the AF Memorial, which overlooks the Pentagon. Tourists site see there. On the day DS commissioned, many visitors were shocked to see a commissioning going on. His school allows cadets to do both a private and the public (det commissioning) oath. There was Bullet commissioning DS, and as I choked back the tears watching the father handing off the torch to the next generation I didn't see the visitors. I was in the moment holding his now fiance's hand. It was only afterwards when I heard a round of applause that I realized there were about 50 people seeing a once in a life time moment. Many actually came up and thanked DS.
That's my story.
Also, for AF parents if your child is going rated, be prepared for a big weekend, when they wing. It is a 3 day affair.