A micro-electro-mechanical system, MEMS, microphone assembly comprises an enclosure defining a first cavity, and a MEMS microphone arranged inside the first cavity. The microphone comprises a first die with bonding structures and a MEMS diaphragm, and a second die having an application specific integrated circuit, ASIC. The second die is bonded to the bonding structures such that a gap is formed between a first side of the diaphragm and the second die, with the gap defining a second cavity. The first side of the diaphragm is interfacing with the second cavity and a second side of the diaphragm is interfacing with the environment via an acoustic inlet port of the enclosure. The bonding structures are arranged such that pressure ventilation openings are formed that connect the first cavity and the second cavity.