Three zeolites systems (ZSM-5, Faujasite Y, Mordenite) were prepared by using a supramolecular surfactant assembly method. Samples were labeled depending on the obtained phase, F (faujasite) and M (ZSM-5), 1 for (Dimethyloctadecyl[3-(trimethoxysilyl)propyl] ammonium chloride (DMOTPAC) and 2 by using cetyltrimethylammonium bromide-polyethylene glycol (CTAB-PEG). The textural properties for supports exhibited a unimodal pore size distribution around 3.9 nm. The TEM images showed the formation of different structures and morphologies, depending on the type of sample. The TPD of NH3 results indicated a clear variation in the quantities of acid sites following the trend F2˃F1˃M2˃M1. These materials were used to support Co-Mo sulfides and they were tested in the hydrodesulfurization (HDS) of dibenzothiophene (DBT). The CoMo catalysts showed the activities trend: CoMo/M1>CoMo/M2>CoMo/F1> CoMo/F2. This behavior resulted in agreement with length and stacking of MoS2 slabs as well as with the NO adsorption amount. The tendency displayed by the surface acidity resulted inverse to the HDS activity and also was inversely proportional to the length and stacking of MoS2 slabs. Thus, the highest the acid sites amount the lowest the slab length and stacking.