The complexation of polyvalent macroions with oppositely charged polyelectrolyte microgels can lead to core-shell structures. The shell is believed to be highly deswollen with a high concentration of counter-macroions. The core is believed to be relatively free of macroions but under a uniform compressive stress due to the deswollen shell. We use cryo-scanning electron microscopy (SEM) with X-ray microanalysis to confirm this understanding. We study poly(acrylic acid) (PAA) microgels which form a core-shell structure when complexed with a small cationic antimicrobial peptide (L5). We follow the spatial distribution of polymer, water, Na counterions, and peptide based on the characteristic X-ray intensities of C, O, Na, and N, respectively. Frozen-hydrated microgel suspensions include buffers of known composition from which calibration curves can be generated and used to quantify both the microgel water and sodium concentrations, the latter with a minimum quantifiable concentration less than 0.048 M. We find that as-synthesized PAA microgels are enriched in Na relative to the surrounding buffer as anticipated from established ideas of counterion shielding of electrostatic charge. The shell in L5-complexed microgels is depleted in Na and enriched in peptide and contains relatively little water. Our measurements furthermore show that shell/core interface is diffuse over a length scale of a few micrometers. Within the limits of detection, the core Na concentration is the same as that in as-synthesized microgels, and the core is free of peptide. The core has a slightly lower water concentration than as-synthesized controls, consistent with the hypothesis that the core is under compression from the shell.