Context. Observations reveal a strong structural coupling between bulge and disc in S0 galaxies, which seems difficult to explain if they have formed from supposedly catastrophic events such as major mergers. Aims. We face this question by quantifying the bulge-disc coupling in dissipative simulations of major and minor mergers that result in realistic S0s. Methods. We have studied the dissipative N-body binary merger simulations from the GalMer database that give rise to realistic, relaxed E/S0 and S0 remnants (67 major and 29 minor mergers). We simulate surface brightness profiles of these S0-like remnants in the K band, mimicking typical observational conditions, to perform bulge-disc decompositions analogous to those carried out in real S0s. Additional components have been included when needed. The global bulge-disc structure of these remnants has been compared with real data. Results. The S0-like remnants distribute in the B/T -r e -h d parameter space consistently with real bright S0s, where B/T is the bulgeto-total luminosity ratio, r e is the bulge effective radius, and h d is the disc scalelength. Major mergers can rebuild a bulge-disc coupling in the remnants after having destroyed the structures of the progenitors, whereas minor mergers directly preserve them. Remnants exhibit B/T and r e /h d spanning a wide range of values, and their distribution is consistent with observations. Many remnants have bulge Sérsic indices ranging 1 < n < 2, flat appearance, and contain residual star formation in embedded discs, a result which agrees with the presence of pseudobulges in real S0s. Conclusions. Contrary to the popular view, mergers (and in particular, major events) can result in S0 remnants with realistically coupled bulge-disc structures in less than ∼3 Gyr. The bulge-disc coupling and the presence of pseudobulges in real S0s cannot be used as an argument against the possible major-merger origin of these galaxies.