Despite many studies of subsurface imaging of carbon nanotube (CNT)-polymer composites via scanning electron microscopy (SEM), significant controversy exists concerning the imaging depth and contrast mechanisms. We studied CNT-polyimide composites and, by three-dimensional reconstructions of captured stereo-pair images, determined that the maximum SEM imaging depth was typically hundreds of nanometers. The contrast mechanisms were investigated over a broad range of beam accelerating voltages from 0.3 to 30 kV, and ascribed to modulation by embedded CNTs of the effective secondary electron (SE) emission yield at the polymer surface. This modulation of the SE yield is due to non-uniform surface potential distribution resulting from current flows due to leakage and electron beam induced current. The importance of an external electric field on SEM subsurface imaging was also demonstrated. The insights gained from this study can be generally applied to SEM nondestructive subsurface imaging of conducting nanostructures embedded in dielectric matrices such as graphene-polymer composites, silicon-based single electron transistors, high resolution SEM overlay metrology or e-beam lithography, and have significant implications in nanotechnology.