  Combining the construction of integrable systems of hydrodynamic type
starting from the Fr\"olicher-Nijenhuis bicomplex $(d,d_L)$ associated with a
(1,1)-tensor field $L$ with vanishing Nijenhuis torsion with the construction
of flat structures starting from integrable systems of hydrodynamic type we
define multi-parameter families of bi-flat structures
$(\nabla,e,\circ,\nabla^*,*,E)$ associated with Fr\"olicher-Nijenhuis
bicomplexes. We call these structures Lauricella bi-flat structures since in
the n-dimensional semisimple case (n-1) flat coordinates of r are Lauricella
functions.
