  This paper is devoted to systematically extend $f$-mirror symmetry between
families of hypersurfaces in complete toric varieties, as introduced in
\cite{R-fTV}, to families of complete intersections subvarieties. Namely,
$f$-mirror symmetry is induced by framed duality of framed toric varieties
extending Batyrev-Borisov polar duality between Fano toric varieties. Framed
duality has been defined and essentially well described for families of
hypersurfaces in toric varieties in the previous \cite{R-fTV}. Here it is
developed for families of complete intersections, allowing us to strengthening
some previous results on hypersurfaces. In particular, the class of projective
complete intersections and their mirror partners are studied in detail.
Moreover, a (generalized) Landau-Ginzburg/Complete-Intersection correspondence
is discussed, extending to the complete intersection setup the LG/CY
correspondence firstly studied Chiodo-Ruan and Krawitz.
