Process integrating two-stage hydrocracking and a hydrotreatment process

A process for hydrocracking hydrocarbon-containing VD feedstocks allowing the improved production of middle distillates: a) hydrocracking of feedstocks in hydrogen and at least one hydrocracking catalyst, b) gas/liquid separation of effluent originating from a) producing a liquid effluent and a gaseous effluent with hydrogen, c) comprising the gaseous effluent before recycling into hydrocracking a), d) fractionation of liquid effluent into at least one effluent of converted hydrocarbon-containing products having boiling points less than 340° C. and an unconverted liquid fraction having a boiling point greater than 340° C., e) hydrocracking unconverted liquid fraction from d), in hydrogen and a hydrocracking catalyst, f) hydrotreating effluent from e) in a mixture with a hydrocarbon-containing gas-oil liquid feedstock having at least 95% by weight of compounds boiling at a boiling point between 150 and 400° C., hydrotreating f) operating in hydrogen and with at least one hydrotreating catalyst.