Context: HIP 96515 A is a double-lined spectroscopic binary included in the SACY catalog as a potential young star. It has a visual companion (CCDM 19371-5134 B, HIP 96515 B) at 8.6 arcsec. If bound to the primary, the optical and infrared colors of this wide companion are consistent with those of a white dwarf. Aims: We attempt to characterize the system HIP 96515 A&B by studying each of its components. Methods: We analyzed spectroscopic and photometric observations of HIP 96515 A and its visual companion, HIP 96515 B. To confirm the system as a common proper-motion pair, we analyzed the astrometry of the components using high-angular resolution infrared observations obtained within a time span of two years, and archival astrometry. Results: The high-resolution optical spectrum of HIP 96515 A was used to derive a mass ratio, M_2/M_1, close to 0.9. The optical lightcurve of HIP 96515 A shows periodic variations with P_orbital = 2.3456 days, revealing that HIP 96515 A is an eclipsing binary with preliminary orbital parameters of i = 89.0° ± 0.2°, and M1 = 0.59 ± 0.03 M&sun; and M2 = 0.54 ± 0.03 M&sun;, for the primary and secondary, respectively, at an estimated distance of 42 ± 3 pc. This is a new eclipsing binary with component masses below 0.6 M&sun;. Multi-epoch observations of HIP 96515 A&B show that the system is a common proper-motion pair. The optical spectrum of HIP 96515 B is consistent with a pure helium atmosphere (DB) white dwarf. The comparison with evolutionary cooling sequence models provides Teff,WD = 19 126 ± 195 K, log gWD = 8.08, MWD/M&sun; = 0.6, and a distance of ~46 pc. The estimated WD cooling age is ~100 Myr and the total age of the object (including the main-sequence phase) is ~400 Myr. Finally, if HIP 96515 A&B are coeval, and assuming a common age of ~400 Myr, the comparison of the masses of the eclipsing binary members with evolutionary tracks shows that they are underestimated by ~15% and 10%, for the primary and secondary, respectively. Based on observations collected at the Paranal Observatory under programs 77.C-0483(A) and 81.C-0826(A).