A counter-flow plate type exchanger is manufactured by repeatedly folding and joining at least two strips of membrane to form a counter-pleated core with a stack of openings or fluid passageways configured in an alternating counter-flow arrangement. Methods for manufacturing such counter-pleated cores are described. Counter-pleated cores comprising water-permeable membranes can be used in a variety of applications, including heat and water vapor exchangers. In particular, they can be incorporated into energy recovery ventilators (ERVs) for exchanging heat and water vapor between air streams directed into and out of buildings, automobiles, or other Industrial processes.