The effect of hygroscopicity of the insulating unit of polymer composites on their response to relative humidity has been investigated. The composites examined were the poly(o-aminophenol) (PoAP) composites with poly(vinyl pyrrolidone) (PVP), poly(acrylic acid) (PAA), poly(ethylene oxide) (PEO), and poly(methyl methacrylate) (PMMA) in which the hygroscopicity of these insulating polymers decreases in the sequence PAA>PVP>PEO>PMMA. The electrical conductivity of the PoAP/PVP composite was proportional to relative humidity covering more than four orders of magnitude. This result is explained on the basis of salt-base transition of conducting polymer in the composite which on reflection depends on the presence of weakly and strongly bound water. The PoAP composite with hydrophilic PAA holds a large amount of strongly bound water, and as a consequence PoAP is completely transformed to the salt form at humidity higher than 70%, resulting in the approach to a constant conductivity at the high level of conduction. On the other hand, the nonlinear dependence of the conductivity upon the change in humidity was observed for the PoAP/PEO and PoAP/PMMA composites on the first run of measurement, which was attributed to a lesser amount of strongly bound water in the composite.