Asymmetric mode hybridization has long remained elusive in wave physics, as mode coupling is typically symmetric in most platforms. Here we show that it can be realized coherently through dual-tone Floquet modulation, in which the relative phase θ of two commensurate drives continuously controls the asymmetry of the coupling between two eigenmodes. We demonstrate this in a strongly coupled cavity magnonic device, where tuning θ reversibly switches single-sided Autler–Townes splitting between the two hybrid modes—a direct spectroscopic signature of phase-programmable asymmetric coupling. Requiring only bichromatic parametric modulation, this coherent approach extends naturally beyond magnonics to other hybrid platforms, opening a new path toward controllable nonreciprocal and topological functionalities for advanced quantum and classical signal processing.