We study the effect of quenched disorder on the behavior of tethered membranes using both analytic and numerical methods. Disorder is introduced via a random spontaneous curvature and a random preferred metric. The presence of impurity-induced spontaneous curvature is found to stiffen the long-wavelength bending rigidity, stabilizing a new disordered flat phase at temperature T=0. This new phase, like that of pure membranes at T>0, is characterized by anomalous statistical and elastic properties. Since its origin is purely mechanical, it can, in principle, be constructed from an appropriate array of macroscopic springs.