The invention provides a composite separator and an electrochemical device such as a battery with the composite separator. The composite separator includes at least one metal-organic framework (MOF) composite layer, and at least one porous layer serving a mechanical support for the at least one MOF composite layer. The at least one MOF composite layer includes at least one MOF material defining a plurality of pore channels and at least one polymer. The at least one MOF material is a class of crystalline porous scaffolds constructed from metal clusters with organic ligands and is activated at a temperature for a period of time such that the at least one MOF material includes unsaturated metal centers, open metal sites and/or structural defects that are able to complex with anions in electrolyte.