The presence of a well-defined and narrow dust lane in an edge-on spiral galaxy is the observational signature of a thin and dense molecular disk, in which gravitational collapse has overcome turbulence. Using a sample of galaxies out to z ∼ 1 extracted from the COSMOS survey, we identify the fraction of massive (L∗ V ) disks that display a dust lane. Our goal is to explore the evolution in the stability of the molecular interstellar medium (ISM) disks in spiral galaxies over a cosmic timescale. We check the reliability of our morphological classifications against changes in rest-frame wavelength, resolution, and cosmic dimming with (artificially redshifted) images of local galaxies from the Sloan Digital Sky Survey. We find that the fraction of L∗ V disks with dust lanes in COSMOS is consistent with the local fraction (≈80%) out to z ∼ 0.7. At z = 0.8, the dust lane fraction is only slightly lower. A somewhat lower dust lane fraction in starbursting galaxies tentatively supports the notion that a high specific star formation rate can efficiently destroy or inhibit a dense molecular disk. A small subsample of higher redshift COSMOS galaxies display low internal reddening (E[B − V ]), as well as a low incidence of dust lanes. These may be disks in which the growth of the dusty ISM disk lags behind that of the stellar disk. We note that at z = 0.8, the most massive galaxies display a lower dust lane fraction than lower mass galaxies. A small contribution of recent mergers or starbursts to this most massive population may be responsible. The fact that the fraction of galaxies with dust lanes in COSMOS is consistent with little or no evolution implies that models to explain the spectral energy distribution or the host galaxy dust extinction of supernovae based on local galaxies are still applicable to higher redshift spirals. It also suggests that dust lanes are long-lived phenomena or can be reformed over very short timescales.