Late stage dynamics of phase separation processes of immiscible binary mixtures containing surfactants (amphiphilic molecules) is investigated by computer simulations on the hybrid model proposed by the present authors [T. Kawakatsu and K. Kawasaki, Physica A 167, 690 (1990)]. With use of this hybrid model, one can investigate large scale phenomena while retaining the intramolecular structures of surfactant molecules. Simulations are performed both for irregular bicontinuous and micellar domain formation processes taking the thermal fluctuation effects into account. In the very late stage, the coarsening of the domain structures is considerably slowed down both for bicontinuous and micellar domain formation processes due to the low interfacial tension of the surfactant-adsorbed interfaces. Scaled scattering structure functions are also calculated, which possess the characteristic features of the experimentally observed scattering functions of microemulsions and polymer blends containing amphiphilic block copolymers. We found that the calculated structure function for the system containing surfactants is different from that for the simple binary mixture without surfactant. Also reported are the important effects of thermal fluctuations on micellar domain structures, where the domain formation is considerably accelerated by the thermal fluctuation.