We derive a general relation between the bosonic and fermionic entanglement in the ground states of supersymmetric quadratic Hamiltonians. For this, we construct canonical identifications between bosonic and fermionic subsystems. Our derivation relies on a unified framework to describe both bosonic and fermionic Gaussian states in terms of so-called linear complex structures J. The resulting dualities apply to the full entanglement spectrum between the bosonic and the fermionic systems, such that the von Neumann entropy and arbitrary Renyi entropies can be related. We illustrate our findings in one- and two-dimensional systems, including the paradigmatic Kitaev honeycomb model. While typically supersymmetry preserves features like area law scaling of the entanglement entropies on either side, we find a peculiar phenomenon, namely, an amplified scaling of the entanglement entropy ("super area law") in bosonic subsystems when the dual fermionic subsystems develop almost maximally entangled modes.