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We present a scheme of reversible waveform conversion between microwave and optical fields in the hybrid opto-electromechanical system. As an intermediate interface, nanomechanical resonator optomechanically couples both optomechanical cavities in the optical and microwave frequency domains. We find the double-optomechanically induced transparency and achieve coherent signal waveform bi-directional transfer between microwave and optical fields based on quantum interference. In addition, we give an analytical expression of one-to-one correspondence between the microwave field and the optical output field, which intuitively shows the reversible waveform conversion relationship. In particular, by numerical simulations and approximate expression, we demonstrate the conversion effects of the three waveforms and discuss the bi-directional conversion efficiency and the bandwidth. such a hybrid opto- and electro-mechanical device has significant potential functions for electro-optic modulation and waveform conversion of quantum microwave-optical field in optical communications and further quantum networks. [ABSTRACT FROM AUTHOR]