Aims. We investigate the relationships between three main optical galaxy observables (spectral properties, colours, and morphology), exploiting the data set provided by the COSMOS/zCOSMOS survey. The purpose of this paper is to define a simple galaxy classification cube, using a carefully selected sample of around 1000 galaxies. Methods. Using medium resolution spectra of the first 1k zCOSMOS-bright sample, optical photometry from the Subaru/COSMOS observations, and morphological measurements derived from ACS imaging, we analyze the properties of the galaxy population out to z~1. Applying three straightforward classification schemes (spectral, photometric, and morphological), we identify two main galaxy types, which appear to be linked to the bimodality of galaxy population. The three parametric classifications constitute the axes of a "classification cube". Results. A very good agreement exists between the classification from spectral data (quiescent/star-forming galaxies) and that based on colours (red/blue galaxies). The third parameter (morphology) is less well correlated with the first two: in fact a good correlation between the spectral classification and that based on morphological analysis (early-/late-type galaxies) is achieved only after partially complementing the morphological classification with additional colour information. Finally, analyzing the 3D-distribution of all galaxies in the sample, we find that about 85% of the galaxies show a fully concordant classification, being either quiescent, red, bulge-dominated galaxies (~20%) or star-forming, blue, disk-dominated galaxies (~65%). These results imply that the galaxy bimodality is a consistent behaviour both in morphology, colour and dominant stellar population, at least out to z~1.