Sheets finished with a hydrophilic polymer which are obtained by applying a fluid containing a hydrophilic polymer to a porous sheet made of paper or nonwoven fabric which sheet comprises 30 to 100% by weight of a hydrophilic fiber by coating or impregnation and converting the polymer on the surface of the sheet and/or inside the sheet into a water-insoluble substance are useful as sheets for total heat exchangers and exhibit higher sensible heat and latent heat conductivities than those of conventional moisture-permeable membrane sheets for total heat exchangers.