A model of hybrid membrane-in cavity is proposed, in which a two-level quantum dot is coupled to the cavity field and the membrane mechanical oscillator at the same time. The bidirectional coupling of quantum dots with cavity field and mechanical oscillator enhances the nonlinear characteristics of the system, which improves the squeezing of the transmitted field and the spontaneous cooling ability of the mechanical oscillator. The results show that the squeezing degree of the transmitted field can be over 90%. With the aid of the quantum dot-mechanical oscillator coupling, an additional squeezing of at least 2% can be obtained. The temperature of the mechanical resonator can be cooled down from room temperature to tens of millikelvin. These operations can be easily controlled by adjusting the power or frequency of the pump light.