Superhydrophobic, porous, 3D materials composed of poly(ϵ-caprolactone) (PCL) and the hydrophobic polymer dopant poly(glycerol monostearate-co-ϵ-caprolactone) (PGC-C18) are fabricated using the electrospinning technique. These 3D materials are distinct from 2D superhydrophobic surfaces, with maintenance of air at the surface as well as within the bulk of the material. These superhydrophobic materials float in water, and when held underwater and pressed, an air bubble is released and will rise to the surface. By changing the PGC-C18 doping concentration in the meshes and/or the fiber size from the micro- to nanoscale, the long-term stability of the entrapped air layer is controlled. The rate of water infiltration into the meshes, and the resulting displacement of the entrapped air, is quantitatively measured using X-ray computed tomography. The properties of the meshes are further probed using surfactants and solvents of different surface tensions. Finally, the application of hydraulic pressure is used to quantify the breakthrough pressure to wet the meshes. The tools for fabrication and analysis of these superhydrophobic materials as well as the ability to control the robustness of the entrapped air layer are highly desirable for a number of existing and emerging applications.