A micro-electro-mechanical actuator device includes a fixed structure and a mobile structure. The mobile structure includes a first deformable band, a second deformable band, and a third deformable band, both of which extend on opposite sides of the first deformable band, each of which carries a piezoelectric actuator. In a working condition, in which the second and third piezoelectrics are biased, the second and third deformable bands are subjected to a negative bending, while the first deformable band is subjected to a positive bending. There are thus generated two translations that add together, causing a displacement of the first deformable band greater than the one that may be obtained by a single membrane of an equal base area.