Multi-layered golf balls containing a two or three-layered cover assembly are provided. In one embodiment, the cover assembly includes a relatively hard inner cover and relatively soft outer cover. Alternatively, the cover assembly may include a relatively soft inner cover with a relatively hard outer cover. Three-layered covers comprising an inner cover, intermediate cover, and outer cover layer also may be prepared. Preferably, at least one of the layers is formed from a thermoplastic composition that preferably comprises: a) ethylene acid copolymer, b) plasticizer, and c) cation source. A fatty acid ester such as ethyl oleate is preferably used as the plasticizer. The cover assembly has good impact durability and helps provide the ball with relatively high resiliency at given compressions.