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 - re - hd parameter space consistently with real bright S0s, where B/T is the bulge-to-total luminosity ratio, re is the bulge effective radius, and hd 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 re/hd spanning a wide range of values, and their distribution is consistent with observations. Many remnants have bulge Sérsic indices ranging 1