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Polarimetry is generally used to determine the polarization state of light beams in various research fields, such as biomedicine, astronomy, and materials science. In particular, the rotating quarter-wave plate polarimeter is an inexpensive and versatile option used in several single-wavelength applications to determine the four Stokes parameters. Extending this technique to broadband spectroscopic measurements is of great scientific interest since the information on light polarization is highly sensitive to anisotropic phenomena. However, the need for achromatic polarizing elements, especially quarter-wave plates, requires special attention in their modeling. In this study, we implemented a rotating retarder spectropolarimeter for broadband measurements using a commercially available quasi-achromatic biplate retarder over the visible range. Here, we present a comprehensive approach for troubleshooting this type of spectropolarimeter through the observation of artifacts stemming from the standard single-plate retarder model. Then, we derive a more suitable model for a quasi-achromatic retarder consisting of a biplate junction. This new biplate model requires knowledge of the intrinsic dispersive properties of the biplate, namely the equivalent retardance, fast axis tilt, and rotatory angle. Hence, in this study, we also show a self-consistent methodology to determine these biplate properties using the same polarimeter apparatus so that accurate Stokes parameters can be determined independently. Finally, the comparison of data generated with the standard single-plate and new biplate models shows a significant improvement in the measurement precision of the investigated polarization states, which confirms that remodeling the retarder for reliable spectropolarimetry is necessary.