  Hard-spin mean-field theory has recently been applied to Ising magnets,
correctly yielding the absence and presence of an interface roughening
transition respectively in $d=2$ and $d=3$ dimensions and producing the
ordering-roughening phase diagram for isotropic and anisotropic systems. The
approach has now been extended to the effects of quenched random pinning
centers and missing bonds on the interface of isotropic and anisotropic Ising
models in $d=3$. We find that these frozen impurities cause domain boundary
roughening that exhibits consecutive thresholding transitions as a function
interaction of anisotropy. For both missing-bond and pinning-center impurities,
for moderately large values the anisotropy, the systems saturate to the
"solid-on-solid" limit, exhibiting a single universal curve for the domain
boundary width as a function of impurity concentration.
