  We employ the periodic Anderson model with superconducting correlations in
the conduction band at half filling to study the behavior of the in-gap bands
in a heterostructure consisting of a molecular layer deposited on the surface
of a conventional superconductor. We use the dynamical mean-field theory to map
the lattice model on the superconducting single impurity model with
self-consistently determined bath and use the continuous-time hybridization
expansion (CT-HYB) quantum Monte Carlo and the iterative perturbation theory
(IPT) as solvers for the impurity problem. We present phase diagrams for square
and triangular lattice that both show two superconducting phases that differ by
the sign of the induced pairing, in analogy to the $0$ and $\pi$ phases of the
superconducting single impurity Anderson model and discuss the evolution of the
spectral function in the vicinity of the transition. We also discuss the
failure of the IPT for superconducting models with spinful ground state and the
behavior of the average expansion order of the CT-HYB simulation.
