DNA-complexes with platelet-like, cationically modified lipid nanoparticles (cLNPs) are studied with regard to the formation of nanocomposite structures with a sandwich-like arrangement of the DNA and platelets. For this purpose suspensions of platelet-like triglyceride nanocrystals, stabilized by a mixture of two nonionic (lecithin plus polysorbate 80 or poloxamer 188) and one cationic stabilizer dimethyldioctadecylammonium (DODAB), are used. The structure of the platelets in the native suspensions and their DNA-complexes, ranging from the sub-nano to the micron scale, is investigated with small-and wideangle scattering (SAXS, SANS, WAXS), calorimetry, photon correlation spectroscopy, transmission electron microscopy and computer simulations. The appearance of strong, lamellarly ordered peaks in the SAXS patterns of the DNA-complexes suggests a stacked arrangement of the nanocrystals, with the DNA being partially condensed between the platelets. This finding is supported with computer simulated small-angle scattering patterns of nanocrystal stacks, which can reproduce the measured small-angle scattering patterns on an absolute scale. The influence of the choice of the nonionic stabilizers and the amount of the cationic stabilizer DODAB on the structure of the native suspensions and the inner structure of their DNA-complexes is studied, too. Using high amounts of DODAB, lecithins with saturated acyl chains and polysorbate 80 instead of poloxamer 188 produces thinner nanocrystals, and thus decreases their repeat distances in the nanocomposites. Such nanocomposites could be of interest as DNA carriers, where the triglyceride platelets protect the sandwiched DNA from degradation.