Optomechanical phenomena in photonic devices provide a new means of light-light interaction mediated by optical force actuated mechanical motion. In cavity optomechanics, this interaction can be enhanced significantly to achieve strong interaction between optical signals in chip-scale systems, enabling all-optical signal processing without resorting to electro-optical conversion or nonlinear materials. However, current implementation of cavity optomechanics achieves both excitation and detection only in a narrow band at the cavity resonance. This bandwidth limitation would hinder the prospect of integrating cavity optomechanical devices in broadband photonic systems. Here we demonstrate a new configuration of cavity optomechanics that includes two separate optical channels and allows broadband readout of optomechanical effects. The optomechanical interaction achieved in this device can induce strong but controllable nonlinear effects, which can completely dominate the device's intrinsic mechanical properties. Utilizing the device's strong optomechanical interaction and its multichannel configuration, we further demonstrate all-optical, wavelength-multiplexed amplification of radio-frequency signals.