There are several grounds over which there exists or should exist an interface between these two disciplines, which some times exist together under one roof (Department), and some times, seperately.
From its very inception, in the 18th c., Indian Archaeology has been more historical than anything else (see Pratap, Forthcoming “On the use of the term non-anglo archaeology”. Archaeologies. December?? 2007. Journal of the World Archaeological Congress).
However, as things stand, archaeological research in India has not developed apace with history as a discipline. Often archaeology is taught as subsets of papers on ancient Indian History, under departments of history, instead of full-fledged departments being set-up for it.