This paper applies multifractal spectrum theory to characterize the structural complexity of 3D surface roughness of copper (II) tetrasulfophthalocyanine (CuTsPc) films on the indium tin oxide (ITO) substrate, obtained with atomic force microscopy (AFM) analysis. CuTsPc films were prepared by drop cast method on ITO substrate. CuTsPc films surface roughness was studied by AFM in tapping-mode™, in air, on square areas of 2500 µm2. A novel approach, on the basis of computational algorithms for analysis of 3D roughness surface applied for AFM data, was presented. Results revealed that the 3D surface roughness of CuTsPc films prepared by drop cast method on ITO substrate can be described using the multifractal geometry. The generalized dimensions Dq and the multifractal spectrum f(α) provided quantitative values that characterize the local scale properties of CuTsPc films surface geometry at nanometer scale. Data provide valuable information to describe the spatial arrangement of 3D surface roughness of CuTsPc films on ITO substrate, which was not taken into account by classical surface statistical parameters. Copyright © 2014 John Wiley & Sons, Ltd.