This work reports on the synthesis of nanosheets of layered titanosilicate JDF-L1 supported on commercial E-type glass fibers with the aim of developing novel nanoarchitectures useful as robust and easy to handle hydrogen adsorbents. The preparation of those materials is carried out by hydrothermal reaction from the corresponding gel precursor in the presence of the glass support. Because of the basic character of the synthesis media, silica from the silicate-based glass fibers can be involved in the reaction, cementing its associated titanosilicate and giving rise to strong linkages on the support with the result of very stable heterostructures. The nanoarchitectures built up by this approach promote the growth and disposition of the titanosilicate nanosheets as a house-of-cards radially distributed around the fiber axis. Such an open arrangement represents suitable geometry for potential uses in adsorption and catalytic applications where the active surface has to be available. The content of the titanosilicate crystalline phase in the system represents about 12 wt %, and this percentage of the adsorbent fraction can achieve, at 298 K and 20 MPa, 0.14 wt % hydrogen adsorption with respect to the total mass of the system. Following postsynthesis treatments, small amounts of Pd (<0.1 wt %) have been incorporated into the resulting nanoarchitectures in order to improve their hydrogen adsorption capacity. In this way, Pd-layered titanosilicate supported on glass fibers has been tested as a hydrogen adsorbent at diverse pressures and temperatures, giving rise to values around 0.46 wt % at 298 K and 20 MPa. A mechanism of hydrogen spillover involving the titanosilicate framework and the Pd nanoparticules has been proposed to explain the high increase in the hydrogen uptake capacity after the incorporation of Pd into the nanoarchitecture.