A two-phase composite of ionically-conductive pressure-sensitive adhesive, biomedical electrodes using the composite and methods of preparing the composite and the electrode are disclosed. The continuous phase is a hydrophilic, solid state pressure-sensitive adhesive composition ionically-conductive regardless of an amount of water present in the composition. The discontinuous phase are domains of a hydrophobic pressure-sensitive adhesive which enhances adhesion of the composite to mammalian skin while maintaining acceptable alternating current impedance of the composite.