A supported and sulphur-containing catalyst is described, comprising; a porous support constituted by an organic-inorganic hybrid material for which the covalent bond between the organic and inorganic phases conforms to the formula M-O—Z—R where M represents at least one metal constituting the inorganic phase, Z at least one heteroelement from among phosphorus and silicon and R an organic fragment, at least one metal of group VIB and/or of group VB and/or of group VIII. The invention also relates to the use of this catalyst for the hydrorefining and the hydroconversion of hydrocarbon-containing feedstocks such as petroleum fractions, fractions from coal or biomass or hydrocarbons produced from natural gas.