A multilayer foam film comprising high density polyethylene for direct and non-direct food contact and aseptic packaging application is disclosed. In an embodiment, the film has a bulk density of less than 0.962 gr/cm3 wherein more than 50% of the cells in the foam layer are closed cells. In an embodiment, the foam films are thick (generally more than 8 mils thick) and have a bending stiffness value of more than 18, in Taber stiffness unit configuration according to TAPPI/ANSI T 489 om-15, and the ratio of the mass per unit area (the mass of a unit area of the film in gram per meter-squared (gr/m2)) over the stiffness value in Taber unit configuration is equal to or less than 13. In an embodiment, the film has a very smooth surface with a smoothness value of less than 25 in Sheffiled smoothness unit configuration according to TAPPI T 538. The described foam film can have a water vapor transmission rate value of less than 1 gr/m2/24 hr, according to ASTM E398-13. The described foam film can have an oxygen transmission rate value of less than 10 cc/m2/24 hr, according to ASTM D3985.