A study on optomechanically induced transparency (OMIT) and the output power at the Stokes (anti‐Stokes) frequency in a hybrid optomechanical system is presented. The system consists of a Fabry–Pérot cavity, two non‐absorbing membranes, and a degenerate optical parametric amplifier (OPA), where the coupling interaction between the cavity and each membrane is quadratic. This study shows that spacing between two transparency window dips in a wider detuning range and the higher transparency efficiency can be achieved by selecting the suitable strength of the quadratic coupling. In addition, it is also found that frequencies of the two mechanical membranes, the nonlinear gain of the OPA, and phase of the field driving OPA can exert a striking influence on the output power at the Stokes (anti‐Stokes) frequency. Specifically, with the increase of the nonlinear parameter of OPA, spacing between two dips on the normalized output power at the Stokes frequency becomes much wider for two membranes with the same frequency. Three peaks on the normalized output power at the anti‐Stokes frequency appear in a larger detuning. In quantum engineering, this scheme may have potential applications in enhancing the performance of OMIT devices. A study on optomechanically induced transparency (OMIT) and the output power at the Stokes (anti‐Stokes) frequency is presented in a hybrid optomechanical system, where the coupling interaction between the cavity and each membrane is quadratic. In quantum engineering, this scheme may have potential applications in enhancing the performance of OMIT devices.