Sheet-like products are disclosed containing an additive composition that enhances various properties of the product. The additive composition, for instance, comprises an aqueous dispersion containing an alpha-olefin polymer, an ethylene-carboxylic acid copolymer, or mixtures thereof. The alpha-olefin polymer may comprise an interpolymer of ethylene and octene, while the ethylene-carboxylic acid copolymer may comprise ethylene-acrylic acid copolymer. The additive composition may also contain a dispersing agent, such as a fatty acid. In one embodiment, the sheet-like product comprises a coform web containing synthetic fibers and pulp fibers.