Aims. We present the results of near-infrared, follow-up imaging and spectroscopic observations at VLT, aimed at characterizing the long-period companions of the exoplanet host stars HD 196885, HD 1237 and HD 27442. The three companions were previously discovered in the course of our CFHT and VLT coronographic imaging survey dedicated to the search for faint companions of exoplanet host stars. Methods. We used the NACO near-infrared adaptive optics instrument to obtain astrometric follow-up observations of HD 196885 A and B. The long-slit spectroscopic mode of NACO and the integral field spectrograph SINFONI were used to carry out a low-resolution spectral characterization of the three companions HD 196885 B, HD 1237 B and HD 27442 B between 1.4 and 2.5 µm. Results. We can now confirm that the companion HD 196885 B is comoving with its primary exoplanet host star, as previously shown for HD 1237 B and HD 27442 B. We find that both companions HD 196885 B and HD 1237 B are low-mass stars of spectral type M1 ± 1V and M4 ± 1V respectively. HD 196885 AB is one of the closer (∼23 AU) resolved binaries known to host an exoplanet. This system is then ideal for carrying out a combined radial velocity and astrometric investigation of the possible impact of the binary companion on the planetary system formation and evolution. Finally, we confirm via spectroscopy that HD 27442 B is a white dwarf companion, the third one to be discovered orbiting an exoplanet host star, following HD 147513 and Gliese 86. The detection of the broad Brγ line of hydrogen indicates a white dwarf atmosphere dominated by hydrogen.