  We extent the recently developed Multi-Layer Multi-Configuration
Time-Dependent Hartree method for Bosons (ML-MCTDHB) for simulating the
correlated quantum dynamics of bosonic mixtures to the fermionic sector and
establish a unifying approach for the investigation of the correlated quantum
dynamics of mixture of indistinguishable particles, be it fermions or bosons.
Relying on a multi-layer wave-function expansion, the resulting Multi-Layer
Multi-Configuration Time-Dependent Hartree method for Mixtures (ML-MCTDHX) can
be adapted to efficiently resolve system-specific intra- and inter-species
correlations. The versatility and efficiency of ML-MCTDHX is demonstrated by
applying it to the problem of colliding few-atom mixtures of both Bose-Fermi
and Fermi-Fermi type. Thereby, we elucidate the role of correlations in the
transmission and reflection properties of the collisional events. In
particular, we present examples where the reflection (transmission) at the
other atomic species is a correlation-dominated effect, i.e.\ it is suppressed
in the mean-field approximation.
