A co-processing combining a first selective catalytic bed consisting of only one metal element selected from group VIB metals and of at least one conventional hydrotreating bimetallic catalytic bed. The co-processing provides control of the hydroconversion reactions of the triglycerides and/or fatty acids of biomass oil diluted in a refinery stream of petroleum hydrocarbons and minimizes the generation of gaseous products that are undesirable to the process, while maintaining the levels of unsaturated hydrocarbons hydrogenation and of heteroatomic contaminants removal from the refinery stream of petroleum hydrocarbons. The co-processing selectively providing n-paraffins of even number of carbon atoms, generated from the biomass oil, which are incorporated in a hydrotreated liquid product in petroleum refining HDT units.