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The phasing problem of heterodyne-detected nonlinear spectroscopy states that the relative time delay between the exciting pulses and a local oscillator must be known with subcycle precision to separate absorptive and dispersive contributions. Here, a solution to this problem is presented which is the time-domain analogue of holographic interferometry, in which the comparison of two holograms reveals changes of an objects size and position with interferometric precision (i.e. to fractions of a wavelength of light). The introduced method, called nonlinear polarization holography, provides equivalent information as attosecond nonlinear polarization spectroscopy but has the advantage of being all-optical instead of using an attosecond streak camera. Nonlinear polarization holography is used here to retrieve the time-domain nonlinear response of a nanoscale iridium film to an ultrashort femtosecond pulse. Using density matrix calculations it is shown that the knowledge of the nonlinear response with subcycle precision allows to distinguish excitation and relaxation mechanisms of low-energetic electrons that depend on the nanoscale structure of the iridium film.