A nonwoven composite that contains a first nonwoven web positioned adjacent to a second nonwoven web is provided. The first nonwoven web contains a plurality of fibers that are formed from a first polyolefin composition, and the second nonwoven web contains a plurality of fibers that are formed from a second polyolefin composition. The first polyolefin composition contains an ethylene polymer, which and car; provide a soft feel to a surface of the first nonwoven web. The second polyolefin composition likewise contains a rigid propylene polymer, which can provide good strength and durability to the second nonwoven web. The second polyolefin composition also contains a ductile propylene polymer and a fatty acid derivative.