The combination of organic and inorganic materials in the nanometric range has driven much research in recent decades, as it enables the production of novel materials and compounds with many potential technological applications. Inorganic porous materials - such as anodic porous alumina (AAO) with its structure of highly-ordered anisotropic channels - have been of particular interest as starting material for several types of devices and functional materials, as well as template and host for organic molecules. In this context, a limiting factor for rationally designing novel organic-inorganic nanomaterials based on inorganic porous materials and polymers is the lack of understanding of the interfacial forces that drive the interactions between the inorganic and organic parts. To address this issue and to gain knowledge of the interaction of polymers and ordered porous materials, here we explored high-resolution non-destructive three-dimensional (3D) imaging in a rational study of the controlled imbibition of melted polymers into porous scaffolds of oxides. For that, we used the Carl Zeiss Xradia 810 Ultra nano-computed tomography scan (nano-CT) that was recently installed in our institute thanks to a large-scale initiative of the Deutsche Forschungsgemeinschaft. Our X-ray nano-CT is equipped with advanced optics that enables absorption-based and phase-contrast imaging with a voxel size of 16 nm and spatial resolution of 50 nm. Different samples of AAO with densely packed, highly ordered, vertically-oriented arrays of pores of 200, 300 or 400 nm diameter was prepared by the anodic oxidation of aluminum. We used polystyrene with two different Mw, which we melted at known temperatures for the experiments under controlled imbibition times. Using X-ray nano-CT, we were able to obtain high-resolution 3D images of the AAO scaffolds and to, therefore, characterize their porosity in detail in a non-destructive way. The volumetric images obtained allow screening the specimen along any virtual plane, showing that nano-CT imaging is an adequate method for finding not only the polymeric imbibition front but also for characterizing the wetting process and understanding the adhesion forces involved in it. Our results show that the method and the device used are ideal to image and resolve the porosity order of the materials analyzed. We anticipate nano-CT imaging as an adequate technique for characterizing novel nanomaterials and for predicting their properties.