Three possible twinning modes, Type I, Type II, and compound, as well as corresponding twin boundaries in 2H martensite of Cu69.4Ni3.4Al27.2 single crystal, were studied by X-ray diffraction (XRD) and high-resolution transmission electron microscopy (HRTEM). The results are discussed with regard to the sharply different twinning stress or twin-boundary mobility. In self-accommodated martensite, all three modes not only coexist but are crystallographically coupled. The compound twin boundary is a coherent coplanar mirror plane with the smallest twinning shear. The Type II twin boundary is also a coherent strain-free interface. The high index rational approximation of Type II twin boundary was determined by trace analysis with the help of stereographic projection. The approximation is in good agreement with irrational indices calculated from elastic continuum. The Type I boundary is the most complex interface associated with high stress and high density of stacking faults inside the twin bands. Using HRTEM, two different stressed boundaries of Type I were confirmed. The intrinsic twinning mode in Cu-Ni-Al alloy is the compound twinning. In compression, the Type II twinning is the major deformation twinning mode. During deformation the Type I twins are eliminated, leaving Type II twinning bands with compound twins. The observed differences between the atomic structure of different twin boundaries can contribute significantly to the sharp differences in twinning stress.