Simultaneously acquired microanalytical X-ray and electron energy loss signals are obtained from a bimetallic core–shell nanoparticle system (FePt@Fe$3$O$4$). The signals are decomposed using independent component analysis and the extracted components are used to separately quantify the composition of the spatially overlapping core and shell phases in the nano-heterostructure. The utilization of the complementary strengths of energy dispersive X-ray and electron energy-loss spectroscopy microanalysis has enabled the quantification of both light and heavy elements in a single spectrum image acquisition.