The chirality of electronic Bloch bands is responsible for many intriguing properties of
layered two-dimensional materials and has been extensively studied in single and few-layers of graphene
and in monolayers of transition metal dichalcogenides (TMDCs). We show that in bilayers of TMDCs,
unlike in few-layer graphene and monolayer TMDCs, both intra-layer and inter-layer couplings give important
contributions to the Berry-curvature in the K and -K valleys of the Brillouin zone. Due to the inter-layer contribution,
the Berry-curvature appears to be gate tunable and also depends on the
stacking of the layers. We point out the differences between the commonly available
3R type and 2H type bilayers and predict the dependence of the valley Hall effect on the stacking type.