Multilayered polymer films are configured so that successive constituent layer packets can be delaminated in continuous sheet form from the remaining film. The films are compatible with known coextrusion manufacturing techniques, and can be made without adhesive layers between layer packets that are tailored to be individually peelable from the remainder of the film. Instead, combinations of polymer compositions are used to allow non-adhesive polymer layers to be combined such that irreversible delamination of the film is likely to occur at interfaces between layer packets pairs. Some of the polymer layers, including at least one embedded layer, comprise an antimicrobial agent, and these layers may be positioned at the front of each layer packet. After the antimicrobial layer of one layer packet has been used, the packet can be peeled away to expose a pristine antimicrobial layer of the next layer packet. The antimicrobial agent may be organic.