We present the multiwavelength properties and catalogue of the 15μm and 1.4GHz radio sources detected in the European Large Area ISO Survey (ELAIS) areas N1 and N2. Using the optical data from the Wide Field Survey we use a likelihood ratio method to search for the counterparts of the 1056 and 691 sources detected at 15μm and 1.4GHz, respectively, down to flux limits of S15= 0.5mJy and S1.4GHz= 0.135mJy. We find that ~92 per cent of the 15μm ELAIS sources have an optical counterpart down to r'= 24. All mid-infrared (IR) sources with fluxes S15>= 3mJy have an optical counterpart. The magnitude distribution of the sources shows a well-defined peak at relatively bright magnitudes r'~ 18. The mid-IR-to-optical and radio-to-optical flux diagrams are presented and discussed in terms of actual galaxy models. About 15 per cent of the sources are bright galactic stars; of the extragalactic objects ~65 per cent are compatible with being normal or starburst galaxies and ~25 per cent active galactic nuclei (AGNs). Objects with mid-IR-to-optical fluxes larger than 100 are found, comprising ~20 per cent of the sample. We suggest that that these sources are highly obscured luminous and ultraluminous starburst galaxies and AGNs.