Sheet-like products, such as tissue products, are disclosed containing an additive composition. 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. The additive composition may be incorporated into the tissue web by being combined with the fibers that are used to form the web. Alternatively, the additive composition may be topically applied to the web after the web has been formed. For instance, in one embodiment, the additive composition may be applied to the web as a creping adhesive during a creping operation. The additive composition may improve the strength of the tissue web and/or improve the perceived softness of the web.