Megan, a definition of a composite structure is
using two or more different materials in a structure to create a single structural unit that functions more effectively than individual materials alone.
Concorde's elevons and rudders utilized a stainless steel honeycomb core sandwiched between aluminum alloy skins. Ergo, a composite structure
and it was the bonding that started to fail.
Ah, I see where the confusion is. A honeycomb structure is not a composite structure. They are 2 different things: one is a construction technique (honeycomb) and one is a class of material (composite). Another construction technique is "laminate".
So, simplistically, a honeycomb can be metal sheets with metal filling, metal sheets with composite filling, composite sheets with metal filling or composite sheets with composite filling. Even metal sheets with paper filling back in the day! All are honeycombs - not composites though some honeycombs may contain composites.
Now, you could refer to it as a generic "composite construction" technique but that leads to confusion with the material "composite" hence why you need to be careful and use the specific construction descriptors such as "honeycomb" or "laminate" to avoid confusion.
But I know how you got there! There has always been a trend to use the word "composite" as a "material" and a "construction technique" interchangeably - since the advent of the "plastic" Sea King blade in my experience. I think that's what you have done. However, that is slack (sorry about that!) usage - and hence the confusion! As I mentioned earlier, this is not helped by the fact the word "composite" has several other uses such as composite floorboards which are really laminates.
That's why, in Aviation, the construction is "honeycomb" or "laminate" but the material class is "metal" or "composite" such as GRP or CF etc, or a mix of both. Hope that helps - it is confusing!