Aerogels based on either clay or cellulose nanofibers are representatives of an emerging class of structural materials with ultra-low density. Both types of aerogels are made from abundant raw materials and are formed through environmentally friendly freeze-drying processes. Due to the ultra-low-density layered superstructure that results from templating by the ice crystal morphology, the neat aerogels are unfortunately often rather fragile. The present study explores inorganic/organic hybrid aerogels that comprise montmorillonite and cellulose nanofibers isolated from tunicates. Dynamic mechanical testing revealed that, especially at low densities, these materials exhibit compressive strengths that are significantly higher than predicted by simple additive behavior of the properties of the individual components. At first glance, the data seem to suggest the formation of a nanoscale "wattle-and-daub'', in which the two components (mud-like clay and straw-like cellulose whiskers) complement each other. It appears that the main cause for this synergy is the enhanced formation of three dimensional network structures during the freeze-drying process.