We present the results of a new and improved study of the morphological and spectral evolution of massive galaxies over the redshift range 1<z<3. Our analysis is based on a bulge-disk decomposition of 396 galaxies with Mstar>10^11 Msolar from the CANDELS WFC3/IR imaging within the COSMOS and UKIDSS UDS survey fields. We find that, by modelling the H(160) image of each galaxy with a combination of a de Vaucouleurs bulge (Sersic index n=4) and an exponential disk (n=1), we can then lock all derived morphological parameters for the bulge and disk components, and successfully reproduce the shorter-wavelength J(125), i(814), v(606) HST images simply by floating the magnitudes of the two components. This then yields sub-divided 4-band HST photometry for the bulge and disk components which, with no additional priors, is well described by spectrophotometric models of galaxy evolution. Armed with this information we are able to properly determine the masses and star-formation rates for the bulge and disk components, and find that: i) from z=3 to z=1 the galaxies move from disk-dominated to increasingly bulge-dominated, but very few galaxies are pure bulges/ellipticals by z=1; ii) while most passive galaxies are bulge-dominated, and most star-forming galaxies disk-dominated, 18+/-5% of passive galaxies are disk-dominated, and 11+/-3% of star-forming galaxies are bulge-dominated, a result which needs to be explained by any model purporting to connect star-formation quenching with morphological transformations; iii) there exists a small but significant population of pure passive disks, which are generally flatter than their star-forming counterparts (whose axial ratio distribution peaks at b/a~0.7); iv) flatter/larger disks re-emerge at the highest star-formation rates, consistent with recent studies of sub-mm galaxies, and with the concept of a maximum surface-density for star-formation activity.