Dramatic irregularities in the plasma density of the ionosphere, first discovered by their effects on radio wave propagation in 1938, and despite decades of investigation, still remain puzzling. Their deleterious effects on radio wave communication, satellite command and control, GPS navigation are serious enough to strongly motivate better understanding of their nature. Many aspects of such irregularities are now understood, but the mechanism(s) of their formation and their detailed nature remain a topic of great interest. In this work, detailed time resolved measurements of lightning generated waves show dispersionless, strongly attenuated propagation with substantial propagation delays. These characteristics of the electromagnetic wave propagation in the two-phase bubble/non-bubble ionosphere parallel the characteristics of acoustic wave propagation through two-phase liquid/vapor foams; and this motivates the suggestion that the bottomside layer of the ionosphere may sometimes be foamy.