Asymmetries of Autler-Townes doublets in resonant photoionization have recently attracted much attention. We show that antiresonances occurring after a field-induced avoided crossing are a novel source of pronounced asymmetry. The mechanism is distinct from the nonlinear dressed-atom stabilization effect recently revealed at extreme ultraviolet wavelengths, because it can arise for atoms that ionize exclusively from the excited state. The ionization rates of dressed states from Floquet theory are explained by an interferometric model. The effect is verified to persist for smooth pulse envelopes through simulations of the time-dependent Schrödinger equation for rubidium in 800 nm laser light. This opens up opportunities to control ionization in new parameter regimes of strong coupling, suitable for alkali atoms hybridized with laser light at optical and near infrared wavelengths.