Mass-energy transfer across the boundaries of living systems is crucial for the maintenance of homeostasis; however, it is scarcely known how structural strength and integrity is maintained in extended phenotypes while also achieving optimum heat-mass exchange. Here we present data on strength, stability, porosity and permeability of termite mounds of a fungus-farming species, Odontotermes obesus. We demonstrate that the termite mound is a bi-layered structure with a dense, strong core and a porous shell that is constantly remodelled. Its safety factor is extraordinarily high and is orders of magnitude higher than those of human constructions. The porous peripheries are analogous to the mulch layer used in agriculture and help in moisture retention crucial for the survival of fungus gardens, while also allowing adequate wind-induced ventilation of the mounds. We suggest that the architectural solutions offered by these termites have wider implications for natural and industrial building technologies.