The chemical composition of protostellar jets and its origin are still badly understood. More observational constraints are needed to make progress. With that objective, we have carried out a systematic search for molecular species in the jet of Cep E-mm, a template for intermediate-mass Class 0 protostars, associated with a luminous, high-velocity outflow. We made use of an unbiased spectral line survey in the range 72-350 GHz obtained with the IRAM 30m telescope, complementary observations of the CO J=3-2 transition with the JCMT, and observations at 1 ′′ angular resolution of the CO J=2-1 transition with the IRAM Plateau de Bure interferometer. In addition to CO, we have detected rotational transitions from SiO, SO, H 2 CO, CS, HCO + and HCN. A strong chemical differentiation is observed in the southern and northern lobes of the jet. Radiative transfer analysis in the Large Velocity Gradient approximation yields typical molecular abundances of the order of 10 −8 for all molecular species other than CO. Overall, the jets exhibit an unusual chemical composition, as CS, SO and H 2 CO are found to be the most abundant species, with a typical abundance of (3-4)×10 −8. The transverse size of the CO jet emission estimated from interferometric observations is about 1000 au, suggesting that we are detecting emission from a turbulent layer of gas entrained by the jet in its propagation and not the jet itself. We propose that some molecular species could be the signatures of the specific photochemistry driven by the UV radiation field generated in the turbulent envelope.