This paper reports on the fabrication and characterization of an inverted Hartmann mask and its application for multi-contrast X-ray imaging of polymer composite material in a laboratory setup. Hartmann masks open new possibilities for high-speed X-ray imaging, obtaining orientation-independent information on internal structures without rotating the object. The mask was manufactured with deep X-ray lithography and gold electroplating on a low-absorbing polyimide substrate. Such an approach allows us to produce gratings with a small period and high aspect ratio, leading to a higher spatial resolution and extension towards higher X-ray energies. Tuning the manufacturing process, we achieved a homogeneous patterned area without supporting structures, thus avoiding losses on visibility. We tested mask performance in a laboratory setup with a conventional flat panel detector and assessed mask imaging capabilities using a tailored phantom sample of various sizes. We performed multi-modal X-ray imaging of epoxy matrix polymer composites reinforced with glass fibers and containing microcapsules filled with a healing agent. Hartmann masks made by X-ray lithography enabled fast-tracking of structural changes in low absorbing composite materials and of a self-healing mechanism triggered by mechanical stress.