Composite webs having a structured web attached to a carrier web and methods of manufacturing the composite webs are disclosed. The structured web may include a plurality of structures that protrude from the structured web. The methods may involve delivering a molten polymeric composition onto the outer surface of a forming tool that includes a plurality of depressions formed in the outer surface. The molten polymer enters depressions in the outer surface of the forming tool and is solidified therein such that a plurality of structures are formed in the shape of the depressions. A skin layer of the polymeric composition may extend between the depressions, such that the structured web formed on the forming tool includes a skin layer connecting the structures. The structured web is removed from the forming tool after solidification of the polymeric composition by adhering the structured web to a carrier web using adhesive located between the carrier web and structured web.