We investigate the sideband spectra of a driven nonlinear mode with its eigenfrequency being modulated at a low frequency (<1 kHz). This additional parametric modulation leads to prominent antiresonance line shapes in the sideband spectra, which can be controlled through the vibration state of the driven mode. We also establish a direct connection between the antiresonance frequency and the squeezing of thermal fluctuation in the system. Our Letter not only provides a simple and robust method for squeezing characterization, but also opens a new possibility toward sideband applications.