  In this paper, we study a system of PDE's describing the motion of two
compressible viscous fluids occupying the whole space $\mathbb {R}^d\;(d\in
\{2,3\}$). We prove a local well-posedness result with discontinuous initial
data: we require the initial density to be H\"older continuous on both sides of
a hyper-surface across which it can experience large jumps. The initial
velocity belongs to the Sobolev space $H^1(\mathbb{R}^d)$ and the divergence of
the initial stress tensor to belong to $L^2(\mathbb{R}^d)$. The later
assumption expresses somehow the continuity of the stress tensor. This result
is more general than the one by Tani [26] by allowing low regular initial data,
and it can be used to serve as building blocks for global solutions.
