  We derive a dynamical mean-field theory for mixtures of interacting bosons
and fermions on a lattice (BF-DMFT). The BF-DMFT is a comprehensive,
thermodynamically consistent framework for the theoretical investigation of
Bose-Fermi mixtures and is applicable for arbitrary values of the coupling
parameters and temperatures. It becomes exact in the limit of high spatial
dimensions d or coordination number Z of the lattice. In particular, the
BF-DMFT treats normal and condensed bosons on equal footing and thus includes
the effects caused by their dynamic coupling. Using the BF-DMFT we investigate
two different interaction models of correlated lattice bosons and fermions, one
where all particles are spinless (model I) and one where fermions carry a spin
one-half (model II). In model I the local, repulsive interaction between bosons
and fermions can give rise to an attractive effective interaction between the
bosons. In model II it can also lead to an attraction between the fermions.
