Monolayers of polynucleic acids at solid-liquid interfaces are widely encountered in biological research and medical diagnostics, and also provide versatile experimental models for elucidating the interfacial behavior of charged polymers. When a time varying potential is applied across a layer of end-tethered DNA chains, between the underlying solid support and bulk solution, the resultant capacitive charging currents provide information on layer organization as well as means for monitoring binding of analyte species in diagnostic applications. Experimental data on the capacitance of DNA monolayers have been obtained over a range of ionic strengths and chain coverages, and interpreted in terms of monolayer organization using concepts from polymer science and a modified Gouy-Chapman theory of double layer capacitance. Retention of counterions by the monolayers manifests as a decreased susceptibility of the capacitance to the external salt environment. Moreover, the charging response exhibits signatures of structural reorganization whereby the DNA strands stretch or relax with changes in solution ionic strength. A method for non-destructive electrochemical quantification of strand coverage, based on shifts in the reduction potential of redox-active counterions associated with the monolayer, was also developed. The shifts are partially an outcome of electrical work needed to bring additional counterions into the monolayer, against a concentration gradient, in order to preserve monolayer electroneutrality when its counterions are reduced.