Continuous carbon fiber polymer-matrix composites in unprecedented antiferroelectric coupling, as enabled by stacking composites with positive value (up to 400) and negative value (down to -600) of the electric permittivity, provide exceptionally high through-thickness permittivity up to 78,000 (a parts per thousand currency sign2.0 MHz), corresponding to a capacitance of 370 mu F/m(2). The high capacitance is consistent with the equation for negative and positive capacitors in series. The permittivity tailoring of the composites involves dielectric cellulosic tissue paper interlaminar interlayers. Negative permittivity (not previously reported for carbon fiber composites) requires the paper to be wet with tap water (resistivity 1.5 ka"broken vertical bar cm) during incorporation in the composite, though the water evaporates and leaves ions at very low concentrations during composite fabrication, and also requires optimum through-thickness resistivity (e.g., 1 ka"broken vertical bar cm, as given by paper thickness 35 mu m); it is probably due to interactions between the functional groups on the carbon fiber surface and the residual ions (mainly chloride) left after tap water evaporation.