We interpret detailed SEM and time-lapse observations of the calcification process in living foraminifera, which we reveal to be directly linked to the construction mechanism of organic membranes where the calcium carbonate precipitation takes place. We show that these membranes are a highly perforated outline is first woven by skeletal pseudopodia and then later overlaid by a layer of membranous pseudopodia to close the gaps. The chemical composition is related to these structures.