The strain and compositional fluctuations of nearly lattice-matched Al0.81In0.19N/GaN heterostructures are investigated by cross-sectional scanning tunneling microscopy and selected area electron diffraction measurements in scanning electron transmission microscopy. The presence of strain induces height modulations governed by different roughness components at the cleavage surfaces. The surface height modulations are compatible with a relaxation of alternatingly compressive and tensile strained domains, indicating compositional fluctuations. Changes of the a lattice constant are traced to interface misfit edge dislocations. The dislocations induce steps increasing the roughness within the Al0.81In0.19N layers. Published by AIP Publishing.