Currently available 3D assemblies based on carbon nanotubes (CNTs) lag far behind their 2D CNT-based bricks and require major improvements for biological applications. By using Fe nanoparticles confined to the interlamination of graphite as catalyst, a fully 3D interconnected CNT web is obtained through the pores of graphene foam (GCNT web) by in situ chemical vapor deposition. This 3D GCNT web has a thickness up to 1.5 mm and a completely geometric, mechanical and electrical interconnectivity. Dissociated cortical cells cultured inside the GCNT web form a functional 3D cortex-like network exhibiting a spontaneous electrical activity that is closer to what is observed in vivo. By coculturing and fluorescently labeling glioma and healthy cortical cells with different colors, a new in vitro model is obtained to investigate malignant glioma infiltration. This model allows the 3D trajectories and velocity distribution of individual infiltrating glioma to be reconstructed with an unprecedented precision. The model is cost effective and allows a quantitative and rigorous screening of anticancer drugs. The fully 3D interconnected GCNT web is biocompatible and is an ideal tool to study 3D biological processes in vitro representing a pivotal step toward precise and personalized medicine.