A filter assembly for a household water filtration apparatus, and a method for filtering water using a household water filtration apparatus are provided. The filter assembly comprises a through-flow cartridge, which has an accessible cavity. The cartridge is removably received in the household water filtration apparatus. The filter assembly further comprises a water permeable enclosure that contains filter media, which is removably received in the accessible cavity. The method comprises opening a through-flow cartridge, depositing a filter packet in the cartridge, closing the cartridge, depositing the cartridge in the household water filtration apparatus, and passing water through the cartridge. Alternately, the filter assembly may be fabricated using polylactic acid.