Context. The surface brightness distribution of ~30-40% of the early-type dwarf galaxies with - 18 ≤ MB ≤ -15 in the Virgo and the Coma clusters is fitted by models that include two structural components (Sérsic + exponential) as for bright disc galaxies. Aims: The goal of the present study is to determine whether early-type dwarf galaxies with a two-component stellar structure in the Virgo and the Coma clusters are low-luminosity copies of bright disc galaxies or are the remnants of bright galaxies strongly transformed by cluster environmental effects. Methods: I analysed the location of bright disc galaxies and early-type dwarfs in the rb,e/h- n plane. The location in this plane of the two-component dwarf galaxies was compared with the remnants of tidally disrupted disc galaxies reported by numerical simulations. Results: Bright unbarred disc galaxies show a strong correlation in the rb,e/h-n plane. Galaxies with larger Sérsic shape parameters show a higher rb,e/h ratio. In contrast, two-component early-type dwarf galaxies do not follow the same correlation. A fraction (~55%) of them are located outside the locus defined in this plane by having 95% of bright disc galaxies. This distribution indicates that they are not a low-mass replica of bright disc galaxies. The different location in the rb,e/h- n plane of two-component early-type dwarfs and bright galaxies can be qualitatively explain whether the former are remnants of disc galaxies strongly transformed by tidal processes. Conclusions: The progenitors of ~20-25% of early-type dwarf galaxies with - 18 ≤ MB ≤ -15 in the Virgo and Coma clusters could be bright disc galaxies transformed by effects of the environment. These tidally transformed galaxies can be selected according to their location in the rb,e/h-n plane.