  The multiconfigurational time-dependent Hartree method (MCTDH) [Chem. Phys.
Lett. {\bf 165}, 73 (1990); J. Chem. Phys. {\bf 97}, 3199 (1992)] is
celebrating nowadays entering its third decade of tackling numerically-exactly
a broad range of correlated multi-dimensional non-equilibrium quantum dynamical
systems. Taking in recent years particles' statistics explicitly into account,
within the MCTDH for fermions (MCTDHF) and for bosons (MCTDHB), has opened up
further opportunities to treat larger systems of interacting identical
particles, primarily in laser-atom and cold-atom physics. With the increase of
experimental capabilities to simultaneously trap mixtures of two, three, and
possibly even multiple kinds of interacting composite identical particles
together, we set up the stage in the present work and specify the MCTDH method
for such cases. Explicitly, the MCTDH method for systems with three kinds of
identical particles interacting via all combinations of two- and three-body
forces is presented, and the resulting equations-of-motion are briefly
discussed. All four possible mixtures of fermions and bosons are presented in a
unified manner. Particular attention is paid to represent the coefficients'
part of the equations-of-motion in a compact recursive form in terms of
one-body density operators only. The recursion utilizes the recently proposed
Combinadic-based mapping for fermionic and bosonic operators in Fock space
[Phys. Rev. A {\bf 81}, 022124 (2010)] and successfully applied and implemented
within MCTDHB. Our work sheds new light on the representation of the
coefficients' part in MCTDHF and MCTDHB without resorting to the matrix
elements of the many-body Hamiltonian with respect to the time-dependent
configurations. It suggests a recipe for efficient implementation of the
schemes derived here for mixtures which is suitable for parallelization.
