Context. Many dense interstellar clouds are observable in emission in the near-IR (J, H, and K photometric bands), commonly referred to as "Cloudshine", and in the mid-IR (Spitzer IRAC 3.6 and 4.5 μm bands), the so-called "Coreshine". These C-shine observations have usually been explained in terms of grain growth but no model has yet been able to self-consistently explain the dust spectral energy distribution from the near-IR to the submm. Aims. Our new core/mantle evolutionary dust model, The Heterogeneous dust Evolution Model at the IaS (THEMIS), has been shown to be valid in the far-IR and submm. We want to demonstrate its ability to reproduce the C-shine observations. Methods. Our starting point is a physically motivated core/mantle dust model. It consists of three dust populations: small polyaromatic-rich carbon grains, bigger core/mantle grains with mantles of aromatic-rich carbon, and cores made of either amorphous aliphatic-rich carbon or amorphous silicate. Then, we assume an evolutionary path where these grains, when entering denser regions, may first form a second aliphatic-rich carbon mantle (coagulation of small grains, accretion of carbon from the gas phase), second coagulate together to form large aggregates, and third accrete gas phase molecules coating them with an ice mantle. To compute the corresponding dust emission and scattering, we use a 3D Monte Carlo radiative transfer code. Results. We show that our global evolutionary dust modelling approach THEMIS allows us to reproduce C-shine observations towards dense starless clouds. Dust scattering and emission is most sensitive to the cloud central density and to the steepness of the cloud density profile. Varying these two parameters leads to changes that are stronger in the near-IR, in both the C-shine intensity and profile. Conclusions. With a combination of aliphatic-rich mantle formation and low-level coagulation into aggregates, we can selfconsistently explain the observed C-shine and far-IR/submm emission towards dense starless clouds.