In the present work, Cu/Cr thin films were deposited on substrates of a different nature (Si, Glass, Bk7, and ITO) through a thermal evaporation deposition method. Non-contact atomic force microscopy (AFM) was used to obtain 3D AFM topographical maps of the surface for the Cu/Cr samples. Various analyses were carried out to obtain crucial parameters for the characterization of the surface features. In particular, Minkowski functionals (including the normalized Minkowski volume, the Minkowski boundary, and the Minkowski connectivity) and studies of the spatial microtexture by fractal and multifractal analyses were carried out. Different roughness parameters (including arithmetical mean height, root mean square height, skewness, kurtosis, fractal dimension, Hurst coefficient, topographical entropy, and fractal lacunarity) were quantified in these analyses for the comparison of the surface morphology of the different samples. All the samples displayed non-Gaussian randomly rough surfaces, indicating the presence of multifractal features.