  We present a formula to compute the Brasselet number of $f:(Y,0)\to (\C, 0)$
where $Y\subset X$ is a non-degenerate complete intersection in a toric variety
$X$. As applications we establish several results concerning invariance of the
Brasselet number for families of non-degenerate complete intersections.
Moreover, when $(X,0) = (\mathbb{C}^n,0)$ we derive sufficient conditions to
obtain the invariance of the Euler obstruction for families of complete
intersections with an isolated singularity which are contained in $X$.
