  Extending our previous work in the strictly parabolic case, we show that a
linearly unstable Lax-type viscous shock solution of a general quasilinear
hyperbolic--parabolic system of conservation laws possesses a
translation-invariant center stable manifold within which it is nonlinearly
orbitally stable with respect to small $L^1\cap H^3$ perturbations, converging
time-asymptotically to a translate of the unperturbed wave. That is, for a
shock with $p$ unstable eigenvalues, we establish conditional stability on a
codimension-$p$ manifold of initial data, with sharp rates of decay in all
$L^p$. For $p=0$, we recover the result of unconditional stability obtained by
Mascia and Zumbrun. The main new difficulty in the hyperbolic--parabolic case
is to construct an invariant manifold in the absence of parabolic smoothing.
