In this paper, the design, optimization and analysis of broadband full-Stokes polarimeters with immunity to both Poisson and Gaussian noise are presented. Different from the commonly-used optimization metrics such as, the condition number (CN), the equally weighted variance (EWV), or the polarimetric modulation efficiency (PME) for Gaussian noise, the optimally balanced condition for Poisson noise (BCPN) is, for the first time, proposed and used as a metric for the optimization of polarimeters. The numerical results show that the polarimeters optimized with the BCPN have immunity to both Poisson and Gaussian noise. The broadband polarimeters optimized from the BCPN are achromatic and have similar polarimetric modulation properties over the waveband, in contrast to the polychromatic polarimeters optimized from the CN, EWV and PME, whose polarimetric modulation properties vary with wavelength.