We compare the details of the distributions of HI, Hα , and far-UV emission in the spiral arms of M81, at a resolution of about 9'' (linear resolution 150 pc at 3.7 Mpc distance). The effects of extinction on the morphology of the Hα and far-UV are shown to be essentially bi-modal, i.e. the extinction is either very small or very large. The observed structures can be understood if ``chimneys'' are common in the spiral arms of M81, where holes are blown out of the galactic disk by star-formation activity similar to that discovered above the Galactic HII region IC1805 by Dewdney and his collaborators at DRAO. We propose further that H2 is turned into HI on a large scale by UV photons impinging on the (rough) surfaces of these chimneys, analogous to the situation proposed to explain the morphology of the Galactic star-forming region G216-2.5 by Williams & Maddalena. In this picture, most of the atomic hydrogen in the inner spiral arms of M81 is UV-dissociated molecular hydrogen from an underlying (and as yet largely undetected) reservoir of molecular gas.