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

A unified ab-initio approach to the correlated quantum dynamics of ultracold fermionic and bosonic mixtures