  We investigate the implications of quantum Darwinism in a composite quantum
system with interacting constituents exhibiting a decoherence-free subspace. We
consider a two-qubit system coupled to an $N$-qubit environment via a dephasing
interaction. For excitation preserving interactions between the system qubits,
an analytical expression for the dynamics is obtained. It demonstrates that
part of the system Hilbert space redundantly proliferates its information to
the environment, while the remaining subspace is decoupled and preserves clear
non-classical signatures. For measurements performed on the system, we
establish that a non-zero quantum discord is shared between the composite
system and the environment, thus violating the conditions of strong Darwinism.
However, due to the asymmetry of quantum discord, the information shared with
the environment is completely classical for measurements performed on the
environment. Our results imply a dichotomy between objectivity and classicality
that emerges when considering composite systems.
