We introduce a novel composite holey gold support that prevents cryo-crinkling and reduces beam-induced motion of soft specimens, building on the previously introduced all-gold support. The composite holey gold support for high-resolution cryogenic electron microscopy of soft crystalline membranes was fabricated in two steps. In the first step, a holey gold film was transferred on top of a molybdenum grid. In the second step, a continuous thin carbon film was transferred onto the holey gold film. This support (Au/Mo grid) was used to image crystalline synthetic polymer membranes. The low thermal expansion of Mo is not only expected to avoid cryo-crinkling of the membrane when the grids are cooled to cryogenic temperatures, but it may also act to reduce whatever crinkling existed even before cooling. The Au/Mo grid exhibits excellent performance with specimens tilted to 45°. This is demonstrated by quantifying beam-induced motion and differences in local defocus values. In addition, images of specimens on the Au/Mo grids that are tilted at 45° show high-resolution information of the crystalline membranes that, after lattice-unbending, extends beyond 1.5 Å in the direction perpendicular to the tilt axis.