A zinc ion-exchanging battery device comprising: (A) a cathode comprising two cathode active materials (a zinc ion intercalation compound and a surface-mediating material); (B) an anode containing zinc metal or zinc alloy; (C) a porous separator disposed between the cathode and the anode; and (D) an electrolyte containing zinc ions that are exchanged between the cathode and the anode during battery charge/discharge. The zinc ion intercalation compound is selected from chemically treated carbon or graphite material having an expanded inter-graphene spacing d002 of at least 0.5 nm, or an oxide, carbide, dichalcogenide, trichalcogenide, sulfide, selenide, or telluride of niobium, zirconium, molybdenum, hafnium, tantalum, tungsten, titanium, vanadium, chromium, cobalt, manganese, iron, nickel, or a combination thereof. The surface-mediating material contains exfoliated graphite or multiple single-layer sheets or multi-layer platelets of a graphene material.