An assembly including a processed cheese portion (22) and a package (26) closely wrapping the portion. The package includes an element which itself comprises a film (2) tightly wrapping the portion and in contact therewith, and tear-initiating member (11) for enabling the sheet (2) to be torn along at least one tear line (8) when a gripping tab (10) of the element is pulled. At least a first part of the or each tear line (8) is defined by or made from a material of the film (2).