A microelectromechanical-acoustic-transducer assembly has: a first die integrating a MEMS sensing structure having a membrane, which has a first surface in fluid communication with a front chamber and a second surface, opposite to the first surface, in fluid communication with a back chamber of the microelectromechanical acoustic transducer, is able to undergo deformation as a function of incident acoustic-pressure waves, and faces a rigid electrode so as to form a variable-capacitance capacitor; a second die, integrating an electronic reading circuit operatively coupled to the MEMS sensing structure and supplying an electrical output signal as a function of the capacitive variation; and a package, housing the first die and the second die and having a base substrate with external electrical contacts. The first and second dice are stacked in the package and directly connected together mechanically and electrically; the package delimits at least one of the front and back chambers.