We study the environmental dependence and the morphological composition of the galaxy color-magnitude diagram at z ~ 0.7, using a pilot subsample of COSMOS. The sample includes ~2000 galaxies with I_AB < 24 and photometric redshift within 0.61 < z < 0.85, covering an area of 270 arcmin². Galaxy morphologies are estimated via a nonparametric automatic technique. The (V - z') versus z' color-magnitude diagram shows a clear red sequence dominated by early-type galaxies and a remarkably well-defined "blue sequence" described by late-type objects. While the percentage of objects populating the two sequences is a function of environment, also following a clear morphology/color-density relation at this redshift, we establish that their normalization and slope are independent of local density. We identify and study a number of objects with "anomalous" colors, given their morphology, polluting the two sequences. Red late-type galaxies are found to be mostly highly inclined or edge-on spiral galaxies for which colors are dominated by internal reddening by dust. In a sample of color-selected red galaxies, these would represent 33% contamination with respect to truly passive spheroidals. Conversely, the population of blue early-type galaxies is composed of objects of moderate luminosity and mass, concurring to only ~5% of the mass in spheroidal galaxies. The majority of them (~70%) occupy a position in the μ_B-r₅₀ plane not consistent with their being precursors of current-epoch elliptical galaxies. Their fraction with respect to the whole galaxy population does not depend on the environment, at variance with the general early-type class. In a color-mass diagram, color sequences are even better defined, with red galaxies covering in general a wider range of masses at nearly constant color, and blue galaxies showing a more pronounced dependence of color on mass. While the red sequence is adequately reproduced by models of passive evolution, the blue sequence is better interpreted as a specific star formation sequence. The substantial invariance of its slope and normalization with respect to local density suggests that the overall "secular" star formation is driven more by galaxy mass than by environment.