A process for manufacturing a composite automobile part by overmoulding, over at least one surface of an insert (1) comprising a first plastic material, a layer of a second thermoplastic material, comprises the following successive steps: a) a step of positioning said insert (1) in a mould, and b) a step of moulding said second thermoplastic material over said insert. At least one of said first and second materials comprises an additive, said additive comprising a polymer to which carboxylic anhydride monomers are grafted. Said first and second materials are respectively based on polyamide and based on polypropylene, or vice versa and said second material comprises talc as mineral filler.