Analysis of eclipsing binaries containing non-radial pulsators allows i) combining two different and independent sources of information on the internal structure and evolutionary status of the components and ii) studying the effects of tidal forces on pulsations. KIC 3858884 is a bright Kepler target whose light curve shows deep eclipses, complex pulsation patterns with pulsation frequencies typical of delta Sct, and a highly eccentric orbit. We present the result of the analysis of Kepler photometry and of high resolution phase-resolved spectroscopy. Spectroscopy yielded both the radial velocity curves and, after spectral disentangling, the primary-component effective temperature and metallicity, and line-of-sight projected rotational velocities. The Kepler light curve was analyzed with an iterative procedure that was devised to disentangle eclipses from pulsations and takes the visibility of the pulsating star into account during eclipses. The search for the best set of binary parameters was performed by combining the synthetic light curve models with a genetic minimization algorithm, which yielded a robust and accurate determination of the system parameters. The binary components have very similar masses (1.88 and 1.86 M-omega) and effective temperatures (6800 and 6600 K), but different radii (3.45 and 3.05 R-omega). The comparison with the theoretical models showed a somewhat different evolutionary status of the components and the need to introduce overshooting in the models. The pulsation analysis indicates the hybrid nature of the pulsating (secondary) component, where the corresponding high order g-modes might be excited by an intrinsic mechanism or by tidal forces.