Simultaneous capillary–gravity solitary waves (simultons or quadratic solitons) are shown to be possible in a rectangular liquid channel of arbitrary finite depth bounded below by a solid plate and above with a free deformable surface with constant surface tension. A second-harmonic resonance between two waveguide modes (fundamental and second-harmonic waves) is studied with the inclusion of dispersion in the system. The nonlinearly coupled amplitude equations for the two slowly varying envelopes of the fundamental and the second-harmonic wave components are derived using the method of multiple scales. Two types of capillary–gravity simulton solutions are explicitly obtained and an experiment for observing such hydrodynamic simultons is suggested.