I'm thinking of my time spent working with cryostats. Liquid helium pot on the inside, and surrounded by a liquid nitrogen jacket. And the whole thing insulated with vacuum and superinsulation. (Superinsulation is many layers of aluminized mylar, which insulates by its reflectivity but must be in a vacuum.) But the point of the liquid nitrogen jacket was to soak up some heat before it got to the liquid helium.
I know boil-off of LH2 is a problem, so I imagine a skinny and insulated LH2 tank literally being inside the LOX tank. But I've never come across that. Has it ever been tried? If not, has it been thought of and rejected for specific reasons?
Edit to clarify and expand:
The theory is that a 90K jacket would preserve LH2 compared with 270K air, and help to protect it from the sun in orbit. During the moon missions, the boil-off in the course of just one extra orbit around the Earth was a Big Deal. It's still a big temperature difference, and the tanks would have to be insulated from each other. Obviously not like a liquid helium dewar, that would be too heavy. But something like the intermediate bulkhead in a Centaur stage.
"Filled with a Styrofoam insulation, the space between the two sheets was pumped clear of air and filled with nitrogen. When fuelled with super-cold propellants, the hydrogen would conduct its low temperature across the thin sheet, freezing out the nitrogen and creating an almost perfect vacuum." (Baker, Rocket:1942 Onwards, Haynes, p. 95).
The porous insulation would support the tanks against the vacuum.
One potential problem: Maybe that would add enough weight that there's no advantage over just making a bigger fuel tank and accepting the boil-off.
One the other hand: Boil-off is a big enough problem that they accepted the weight of a weather shield on the Centaur.
Another potential problem: If they have a weather shield anyway, maybe it's insulated well enough without having to create a dewar-like configuration, with a vacuum-tight space that size, and etc. And the weather shield was meant to be ejected to save weight.
Wait... did I answer my own question?