We have constructed a mass-selected sample of Mstar>10^11Msolar galaxies at 1<z<3 in the CANDELS UDS and COSMOS fields and have decomposed these systems into their separate bulge and disk components according to their H(160)-band morphologies. By extending this analysis to multiple bands we have been able to conduct individual bulge and disk component SED fitting which has provided us with stellar-mass and star-formation rate estimates for the separate bulge and disk components. These have been combined with size measurements to explore the evolution of these massive high-redshift galaxies. By utilising the new decomposed stellar-mass estimates, we confirm that the bulge components display a stronger size evolution than the disks. This can be seen from both the fraction of bulge components which lie below the local relation and the median sizes of the bulge components, where the bulges are a median factor of 2.93+/-0.32 times smaller than similarly massive local galaxies at 1<z<2 and 3.41+/-0.58 smaller at 2<z<3; for the disks the corresponding factors are 1.65+/-0.14 and 1.99+/-0.25. Moreover, by splitting our sample into the passive and star-forming bulge and disk sub-populations and examining their sizes as a fraction of their present-day counter-parts, we find that the star-forming and passive bulges are equally compact, star-forming disks are larger, while the passive disks have intermediate sizes. This trend is not evident when classifying galaxy morphology on the basis of single-Sersic fits and adopting the overall star-formation rates. Finally, by evolving the star-formation histories of the passive disks back to the redshifts when the passive disks were last active, we show that the passive and star-forming disks have consistent sizes at the relevant epoch. These trends need to be reproduced by any mechanisms which attempt to explain the morphological evolution of galaxies.