High-harmonic spectroscopy uses attosecond techniques to measure single-atom or molecule photorecombination cross-sections. Whereas the amplitude of the extreme-ultraviolet light is easily measurable, the phase is more challenging to access. However, the phase contains information necessary for tomographic imaging of the molecular orbital wavefunction with attosecond–ångström resolution. Present techniques cannot simultaneously measure the phase as a function of molecular angle and photon frequency, which is necessary for a full reconstruction of the wavefunction. We overcome this limitation with an all-optical method that does not require any ad hoc assumptions about the phase. We apply it to record the full phase map of aligned bromine molecules relative to reference xenon atoms. It allows us to resolve, both spectrally and angularly, the participation of multiple molecular orbitals, and infer a phase of ionization. This method opens a path to time-resolved molecular orbital tomography. High-harmonic spectroscopy provides attosecond-scale information about optical processes in molecules. Present techniques, however, cannot simultaneously measure the phase as a function of molecular angle and photon frequency. An approach that retrieves both the amplitude and the phase of high-harmonic emission is now demonstrated, and could enable a full reconstruction of the molecular wavefunction.