Context. Intermediate-mass (IM) protostars provide a bridge between the low- and high-mass protostars. Despite their relevance, little is known about their chemical diversity. Aims. We want to investigate the molecular richness towards the envelope of I-M protostars and to compare their properties with those of low- and high-mass sources. Methods. We have selected the isolated IM Class 0 protostar Cep E-mm to carry out an unbiased molecular survey with the IRAM 30 m telescope between 72 and 350 GHz with an angular resolution lying in the range 7–34″. Our goal is to obtain a census of the chemical content of the protostellar envelope. These data were complemented with NOEMA observations of the spectral bands 85.9–89.6 GHz and 216.8–220.4 GHz at angular resolutions of 2.3″ and 1.4″, respectively. Results. The 30 m spectra show bright emission of O- and N-bearing complex organic molecules (COMs): CH₃OH and its rare isotopologues CH₂DOH and ¹³CH₃OH, CH₃CHO, CH₃OCH₃, CH₃COCH₃, HCOOH, HCOOCH₃, H₂CCO, NH₂CHO, CH₃CN, C₂H₃CN, C₂H₅CN, HNCO and H₂CO. We identify up to three components in the spectral signature of COMs: an extremely broad line (eBL) component associated with the outflowing gas (FWHM > 7kms⁻¹), a narrow line (NL) component (FWHM < 3kms⁻¹) associated with the cold envelope, and a broad line (BL) component (FWHM ≃ 5.5kms⁻¹) which traces the signature of a hot corino. The eBL and NL components are detected only in molecular transitions of low excitation and dominate the emission of CH₃OH. The BL component is detected in highly excited gas (E_up > 100 K). The NOEMA observations reveal Cep E-mm as a binary protostellar system, whose components, Cep E-A and Cep E-B, are separated by ≈1.7″. Cep E-A dominates the core continuum emission and powers the long-studied, well-known, high-velocity jet associated with HH377. The lower flux source Cep E-B powers another high-velocity molecular jet, reaching velocities of ≈80 km s⁻¹, which propagates in a direction close to perpendicular with respect to the Cep E-A jet. Our interferometric maps show that the emission of COMs arises from a region of ≈0.7″ size around Cep E-A, and corresponds to the BL component detected with the IRAM 30 m telescope. On the contrary, no COM emission is detected towards Cep E-B. We have determined the rotational temperature (T_rot) and the molecular gas column densities from a simple population diagram analysis or assuming a given excitation temperature. Rotational temperatures of COMs emission were found to lie in the range 20−40 K with column densities ranging from a few times 10¹⁵ cm⁻² for O-bearing species, down to a few times 10¹⁴ cm⁻² for N-bearing species. Molecular abundances are similar to those measured towards other low- and intermediate-mass protostars. Ketene (H₂CCO) appears as an exception, as it is found significantly more abundant towards Cep E-A. High-mass hot cores are significantly less abundant in methanol and N-bearing species are more abundant by two to three orders of magnitude. Conclusions. Cep E-mm reveals itself as a binary protostellar system with a strong chemical differentiation between both cores. Only the brightest component of the binary is associated with a hot corino. Its properties are similar to those of low-mass hot corinos.