  Let $\mathfrak g$ be either the Lie superalgebra
$\mathfrak{gl}(V)\oplus\mathfrak{gl}(V)$ where $V:=\mathbb C^{m|n}$ or the Lie
superalgebra $\mathfrak{gl}(V)$ where $V:=\mathbb C^{m|2n}$. Furthermore, let
$W$ be the $\mathfrak g$-module defined by $W:=V\otimes V^*$ in the former case
and $W:=\mathcal S^2(V)$ in the latter case. Associated to $(\mathfrak g,W)$
there exists a distinguished basis of Capelli operators
$\left\{D^\lambda\right\}_{\lambda\in\Omega}$, naturally indexed by a set of
hook partitions $\Omega$, for the subalgebra of $\mathfrak g$-invariants in the
superalgebra $\mathcal{PD}(W)$ of superdifferential operators on $W$.
  Let $\mathfrak b$ be a Borel subalgebra of $\mathfrak g$. We compute
eigenvalues of the $D^\lambda$ on the irreducible $\mathfrak g$-submodules of
$\mathcal{P}(W)$ and obtain them explicitly as the evaluation of the
interpolation super Jack polynomials of Sergeev--Veselov at suitable affine
functions of the $\mathfrak b$-highest weight. While the former case is
straightforward, the latter is significantly more complex. This generalizes a
result by Sahi, Salmasian and Serganova for these cases, where such formulas
were given for a fixed choice of Borel subalgebra.
