Electromagnetic wave propagation through complex inhomogeneous walls introduces significant distortions to through-wall radar signatures. Estimation of wall thickness, dielectric, and conductivity profiles may enable wall effects to be deconvolved from target scattering. We propose to use deep neural networks (DNNs) to estimate wall characteristics from broadband scattered electric fields on the same side of the wall as the transmitter. We demonstrate that both single deep artificial and convolutional neural networks and dual networks involving generative adversarial networks are capable of performing the highly nonlinear regression operation of electromagnetic inverse scattering for wall characterization. These networks are trained with simulation data generated from full wave solvers and validated on both simulated and real wall data with approximately 95% accuracy.