I think you're picking hairs. While NSA is not strictly a military branch, NSA is a defense agency within the DoD. It is not directed by a civilian, but by a commissioned officer of the military. That seems pretty damned close enough to me.
> the vast majority of its member agencies are all civilian agencies
I don't know how you came to this conclusion, as the actual numbers and ratio of military vs. civilian personnel is still classified to the best of my knowledge. To the best of my (circumstantial) knowledge, the ratio for civilian vs. (usually US Navy) military personnel is likely somewhere around 60/40. I couldn't tell you which category is civilian vs. military, though.
> the person who heads it up (Secretary of Defense) is a civilian.
No, the person who heads it up is an Admiral in the Navy: https://en.wikipedia.org/wiki/Michael_S._Rogers
The SECDEF oversees the DoD as a whole.
I'd love to know how you came up with your conclusions, as you seem to have some familiarity with the Beltway, because they don't match my experiences.