The invention concerns a process for preparing a complex sheet comprising a layer of drylaid glass fibers and a layer of organic fibers, comprising: mechanical needling or fluid entanglement, e.g. hydroentanglement, of a nonwoven fabric of continuous organic fibers and of a veil of non-preconsolidated continuous glass fibers, the said nonwoven fabric of organic fibers and the said veil of glass fibers being juxtaposed and the said needles respectively the fluid, water jets being sent from the same side as the nonwoven fabric of organic fibers, in order to make a sheet; and then application of a binder to the bilayer. The so obtained complex fibrous structure shows a low tendency to delaminate and can be impregnated with asphalt or bitumen, and used in the field of roofing, sealing covering or membranes.