  We prove $f$-positivity of $\mathcal{O}_X(1)$ for arbitrary dimension
fibrations over curves $f\colon X\to B$ whose general fibre is a complete
intersection. In the special case where the family is a global complete
intersection, we prove numerical sufficient and necessary conditions for
$f$-positivity of powers of $\mathcal{O}_X(1)$ and for the relative canonical
sheaf. From these results we also derive a Chow instability condition for the
fibres of relative complete intersections in the projective bundle of a
$\mu-$unstable bundle.
