A golf ball includes a thermoplastic HNP inner core layer having a center hardness less than the surface hardness to define a positive hardness gradient. An outer core layer is formed from a thermoset rubber composition. The core layer has an inner surface hardness less than the outer surface hardness to define a positive hardness gradient of 3 to 30 Shore D. Inner and outer cover layers are disposed about the outer core layer. The HNP composition includes an acid copolymer of ethylene and an α,β-unsaturated carboxylic acid; a non-acid polymer comprising polyolefins, polyamides, polyesters, polyethers, polyurethanes, metallocene-catalyzed polymers, single-site catalyst polymerized polymers, ethylene propylene rubber, ethylene propylene diene rubber, styrenic block copolymer rubbers, alkyl acrylate rubbers, or functionalized derivatives thereof; an organic acid or salt thereof; and a cation source in an amount sufficient to neutralize at least about 80% of the acid groups.