  The interaction of intralayer and interlayer excitons is studied in a
two-dimensional semiconductor, homobilayer MoS$_2$. It is shown that the
measured optical susceptibility reveals both the magnitude and the sign of the
coupling constants. The interlayer exciton interacts capacitively with the
intralayer B-exciton (positive coupling constant) consistent with hole
tunnelling from one monolayer to the other. Conversely, the interlayer exciton
interacts inductively with the intralayer A-exciton (negative coupling
constant). First-principles many-body calculations show that this coupling
arises via an intravalley exchange-interaction of A- and B-excitons.
