We analyse the morphological structures in galaxies of the ATLAS3D sample by fitting a single Sérsic profile and decomposing all non-barred objects (180 of 260 objects) in two components parametrized by an exponential and a general Sérsic function. The aim of this analysis is to look for signatures of discs in light distributions of nearby early-type galaxies and compare them to kinematic properties. Using Sérsic index from single-component fits for a distinction between slow and fast rotators, or even late- and early-type galaxies, is not recommended. Assuming that objects with n > 3 are slow rotators (or ellipticals), there is only a 22 per cent probability to correctly classify objects as slow rotators (or 37 per cent of previously classified as ellipticals). We show that exponential sub-components, as well as light profiles fitted with only a single component of a low Sérsic index, can be linked with the kinematic evidence for discs in early-type galaxies. The median disc-to-total light ratio for fast and slow rotators is 0.41 and 0.0, respectively. Similarly, the median Sérsic indices of the bulge (general Sérsic component) are 1.7 and 4.8 for fast and slow rotators, respectively. Overall, discs or disc-like structures are present in 83 per cent of early-type galaxies which do not have bars, and they show a full range of disc-to-total light ratios. Discs in early-type galaxies contribute with about 40 per cent to the total mass of the analysed (non-barred) objects. The decomposition into discs and bulges can be used as a rough approximation for the separation between fast and slow rotators, but it is not a substitute, as there is only a 59 per cent probability to correctly recognize slow rotators. We find trends between the angular momentum and the disc-to-total light ratios and the Sérsic index of the bulge, in the sense that high angular momentum galaxies have large disc-to-total light ratios and small bulge indices, but there is none between the angular momentum and the global Sérsic index. We investigate the inclination effects on the decomposition results and confirm that strong exponential profiles can be distinguished even at low inclinations, but medium-size discs are difficult to quantify using photometry alone at inclinations lower than ∼50°. Kinematics (i.e. projected angular momentum) remains the best approach to mitigate the influence of the inclination effects.We also find weak trends with mass and environmental density, where disc-dominated galaxies are typically less massive and found at all densities, including the densest region sampled by the ATLAS3D sample.