A thin film BiFeO3 – CoFe2O4 multiferroic nanocomposite has been investigated to determine the coupling between the two phases in a constrained film by combining piezoelectric force microscopy and an externally applied magnetic field. In addition, finite element modeling was carried out to fully explain the observed local piezoelectric response. The results of the experiments and modeling show that the mechanical contributions dominate the local response of the ferroelectric phase and that large regions of high response are due to the interactions of the microstructural features. Also, microstructures that would improve mulitferroic properties are suggested based on the modeled response of the nanocomposite.