Biogenic ceramics are known to exhibit superior toughness due to a laminated architecture with ultrathin organic layers separating the ceramic blocks. Theoretical analyses relate the toughness increase to the modulus contrast, E_c/E_o between the stiff, E_c, and the compliant, E_o, components. However, experimental data on this contrast are extremely difficult to obtain by any known technique due to the very small thickness and low modulus values of the organic layers. Here we adapt a recently developed nanoscale modulus mapping technique combined with reverse finite element analysis in order to map the elastic modulus across a 35 nm thick organic layer within biosilica in a giant anchor spicule of the glass sponge Monorhaphis chuni. We find a modulus of 0.7 GPa in the organic layer as compared to 37 GPa in the bioglass. Furthermore, a modulus gradient extends 50 nm into the glass layer, probably due to the spatial distribution of small organic inclusions. With this new methodology it becomes possible to determine the elastic moduli of nanometric inclusions even when embedded in a matrix which is 50 times stiffer.