A cultivation bag assembly for the cultivation of microbes, fungi and other organisms includes an inner bag for containing a food substrate and an organism to be cultivated. At least one wall of the inner bag is constructed of a layer of water-vapor permeable material. An outer bag of the assembly has first and second walls formed from gas impermeable layers. At least one of the first and second walls of the outer bag has a gas filter patch to allow the passage of oxygen and carbon dioxide gases into and out of the interior of the inner bag to facilitate incubation of the organism within the interior of the inner bag. The inner bag and outer bag are coupled together at a first end of each of the inner bag and outer bag.