We extend the ideas of wave-packet interferometry to implement the algorithm of spectral phase interferometry for direct electric-field reconstruction (SPIDER) for characterizing the amplitude and phase of electron wave packets. Single-photon ionization by an attosecond pulse launches an electron wave packet in the continuum. Ionization by a train of two attosecond pulses in the presence of a moderate infrared pulse creates an interferogram in the final photoelectron momentum distribution. From the interferogram, the complex electron wave function can be reconstructed. If the pulses are well characterized, the amplitude and phase of the bound-free dipole matrix element can be reconstructed over a wide energy range. This is demonstrated by application of the retrieval method to momentum distributions obtained by numerical solution of the time-dependent Schrödinger equation. The case of Coulombic potentials requires appropriate treatment of the laser-Coulomb coupled dynamics. © 2013 American Physical Society.