The first three-dimensional global model in which time-dependent spectral albedos and emissivities over snow and sea ice are predicted with a radiative transfer solution, rather than prescribed, is applied to study the climate response of fossil fuel plus biofuel black carbon plus organic matter (ff+bf BC+OM) when BC absorption in snow and sea ice is accounted for. The model treats the cycling of size-resolved BC+OM between emission and removal by dry deposition and precipitation from first principles. Particles produce and enter size-resolved clouds and precipitation by nucleation scavenging and aerosol-hydrometeor coagulation. Removal brings BC to the surface, where internally and externally mixed BC in snow and sea ice affects albedo and emissivity through radiative transfer. Climate response simulations were run with a ff+bf BC+OC emission inventory lower than that used in a previous study. The 10-year, globally averaged ff+bf BC+OM near-surface temperature response due to all feedbacks was about +0.27 K (+0.32 in the last 3 years), close to those from the previous study (5-year average of +0.3 K and fifth-year warming of +0.35 K) and its modeled range (+0.15 to +0.5 K) because warming due to soot absorption in snow and sea ice here (10-year average of +0.06 K with a modeled range of +0.03 to +0.11 K) offset reduced warming due to lower emission. BC was calculated to reduce snow and sea ice albedo by ∼0.4% in the global average and 1% in the Northern Hemisphere. The globally averaged modeled BC concentration in snow and sea ice was ∼5 ng/g; that in rainfall was ∼22 ng/g. About 98% of BC removal from the atmosphere was due to precipitation; the rest was due to dry deposition. The results here support previous findings that controlling ff+bf BC+OM and CO2 emission may slow global warming.