We have constructed a mass-selected sample of M * > 1011 M⊙ galaxies at 1 < z < 3 in the CANDELS UKIDSS UDS and COSMOS fields and have decomposed these systems into their separate bulge and disc components according to their H 160-band morphologies. By extending this analysis to multiple bands, we have been able to conduct individual bulge and disc component SED fitting which has provided us with stellar-mass and star formation rate estimates for the separate bulge and disc components. Having utilized the new decomposed stellar-mass estimates, we confirm that the bulge components display a stronger size evolution than the discs. The median sizes of the bulge components is 3.09 ± 0.20 times smaller than similarly massive local galaxies over the full 1 < z < 3 redshift range; for the discs, the corresponding factor is 1.77 ± 0.10. Moreover, by splitting our sample into the passive and star-forming bulge and disc 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 discs are larger, while the passive discs have intermediate sizes. This trend is not evident when classifying galaxy morphology on the basis of single-Sérsic fits and adopting the overall star formation rates. Finally, by evolving the star formation histories of the passive discs back to the redshifts when the passive discs were last active, we show that the passive and star-forming discs 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.