Whilst looking for information regarding Shuttle's External Tank insulation, I came across this answer to this question Structural composition of shuttle liquid fuel tank wall.
The answer states that for Super Light-Weight Tank (the third version of it):
the innermost layer is approx 0.1" thickness of Al-Li alloy. The thickness varies along the length of the tank due to varying hydrostatic loads. Outside this there is approx 0.5" of epoxy and then ~2" of foam insulation.
The other answer (to the same question) contains some discussion to the role of epoxy layer, but without definitive conclusion.
So, to me this is still unanswered question: what was the primary role for this epoxy layer (and why is it so thick)?
From one side, it indeed seems way too thick to serve as adhesive primer for the foam (paint with thickness of an order of magnitude smaller was discarded for weight benefits...); from the other side, mechanical strenght of epoxy (without any kind of embedded internal honeycomb) would not be high enough to serve the structural purpose.
A mid-layer to "smoothen" different thermal expansion rates between aluminum alloy and the foam, maybe?