Cirrus cloud absorption optical depths retrieved at 12.05 μm are compared to extinction optical depths retrieved at 0.532 μm from perfectly co-located observations of single-layered semi-transparent cirrus over ocean made by the Imaging Infrared Radiometer (IIR) and the Cloud and Aerosol Lidar with Orthogonal Polarization (CALIOP) flying on board the CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations) satellite. IIR infrared absorption optical depths are compared to CALIOP visible extinction optical depths when the latter can be directly derived from the measured apparent two-way transmittance through the cloud. An evaluation of the CALIOP multiple scattering factor is inferred from these comparisons after assessing and correcting biases in IIR and CALIOP optical depths reported in version 3 data products. In particular, the blackbody radiance taken in the IIR version 3 algorithm is evaluated, and IIR retrievals are corrected accordingly. Numerical simulations and IIR retrievals of ice crystal sizes suggest that the ratios of CALIOP extinction and IIR absorption optical depths should remain roughly constant with respect to temperature. Instead, these ratios are found to increase quasi-linearly by about 40 % as the temperature at the layer centroid altitude decreases from 240 to 200 K. It is discussed that this behavior can be explained by variations of the multiple scattering factor ηT applied to correct the measured apparent two-way transmittance for contribution of forward-scattering. While the CALIOP version 3 retrievals hold ηT fixed at 0.6, this study shows that ηT varies with temperature (and hence cloud particle size) from ηT = 0.8 at 200 K to ηT = 0.5 at 240 K for single-layered semi-transparent cirrus clouds with optical depth larger than 0.3. The revised parameterization of ηT introduces a concomitant temperature dependence in the simultaneously derived CALIOP lidar ratios that is consistent with observed changes in CALIOP depolarization ratios and particle habits derived from IIR measurements.