A new composite material consisting of amorphous TUD-1 encapsulating crystalline zeolite Y was synthesized. Samples with different HY zeolite loadings (10, 20, 40, and 60 wt %) were prepared, and the resulting solid products were characterized with elemental analysis, XRD, N2 physisorption, 27Al MAS NMR, IR, pyridine adsorption in combination with FTIR, temperature-programmed desorption of ammonia, HRSEM, and HRTEM. Characterization data confirm the presence of a thin layer of the mesoporous TUD-1 phase with a thickness of 30–100 nm surrounding the zeolite crystals. The catalytic performance of the composite was studied in the Friedel–Crafts benzylation of benzene with benzyl alcohol at 353 K. The catalytic activity of the HY/TUD-1 composite was higher than that of HY zeolite, whereas the composite showed a much slower rate of deactivation. The improved performance of the composite is related to beneficial changes in the acidity of the HY crystal through chemical interactions with TUD-1.