  Bandstructure engineering using alloying is widely utilised for achieving
optimised performance in modern semiconductor devices. While alloying has been
studied in monolayer transition metal dichalcogenides, its application in van
der Waals heterostructures built from atomically thin layers is largely
unexplored. Here, we fabricate heterobilayers made from monolayers of WSe$_2$
(or MoSe$_2$) and Mo$_x$W$_{1-x}$Se$_2$ alloy and observe nontrivial tuning of
the resultant bandstructure as a function of concentration $x$. We monitor this
evolution by measuring the energy of photoluminescence (PL) of the interlayer
exciton (IX) composed of an electron and hole residing in different monolayers.
In Mo$_x$W$_{1-x}$Se$_2$/WSe$_2$, we observe a strong IX energy shift of
$\approx$100 meV for $x$ varied from 1 to 0.6. However, for $x<0.6$ this shift
saturates and the IX PL energy asymptotically approaches that of the indirect
bandgap in bilayer WSe$_2$. We theoretically interpret this observation as the
strong variation of the conduction band K valley for $x>0.6$, with IX PL
arising from the K-K transition, while for $x<0.6$, the bandstructure
hybridization becomes prevalent leading to the dominating momentum-indirect K-Q
transition. This bandstructure hybridization is accompanied with strong
modification of IX PL dynamics and nonlinear exciton properties. Our work
provides foundation for bandstructure engineering in van der Waals
heterostructures highlighting the importance of hybridization effects and
opening a way to devices with accurately tailored electronic properties.
