We experimentally identify mirror mode (MM) structures in the Voyager 1 heliosheath data for the first time. This is done using the magnetic field data alone. The heliosheath MM structures are found to have the following characteristics: (1) quasiperiodic spacings with a typical scale size of ∼57 ρp, (2) little or no angular changes across the structures (∼3° longitude and ∼3° latitude), and (3) a lack of sharp boundaries at the magnetic dip edges. It is demonstrated that the pickup of interstellar neutrals in the upstream region of the termination shock (TS) and quasiperpendicular TS plasma compression are the causes of MM instability during intervals when the IMF is nearly orthogonal to the solar wind flow direction. Concomitant additional injection of pickup ions (PUIs) throughout the heliosheath will lead to further MM amplification. MM structures in planetary magnetosheaths and interplanetary sheaths are discussed for comparative purposes. Multiple sources of free energy are often involved.