The reconstruction of ultrashort optical pulses with a complex intensity substructure is demonstrated using the Self-Referenced Spectral Interferometry (SRSI) pulse characterization technique with a modified phase retrieval algorithm. A correction spectral phase term is extracted by the manipulation of the temporal interferogram, allowing the treatment of scenarios with complicated pulse shapes, where the original algorithm fails. The improved SRSI algorithm is verified through the application on two temporally well-separated pulses having the same polarization direction and spectral shape, generated by duplicating 37 fs-long amplified pulses of a Ti:Sa based laser system. The spectral phase of highly chirped double pulses with equal or different amplitude ratios is numerically retrieved. The collinear and achromatic experimental arrangement results in a compact and easy-to-align system.