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Our previous model (NEOMOD2) for the orbital and absolute magnitude distribution of Near Earth Objects (NEOs) was calibrated on the Catalina Sky Survey observations between 2013 and 2022. Here we extend NEOMOD2 to include visible albedo information from the Wide-Field Infrared Survey Explorer. The debiased albedo distribution of NEOs can be approximated by the sum of two Rayleigh distributions with the scale parameters 𝑝V,dark ≃ 0.03 and 𝑝V,bright ≃ 0.17. We find evidence for smaller NEOs having (on average) higher albedos than larger NEOs; this is likely a consequence of the size-dependent sampling of different main belt sources. These inferences and the absolute magnitude distribution from NEOMOD2 are used to construct the debiased size distribution of NEOs. We estimate 830±60 NEOs with diameters 𝐷 > 1 km and 20,000±2,000 NEOs with 𝐷 > 140 m. The new model, NEOMOD3, is available via the NEOMOD Simulator — an easy-to-operate code that can be used to generate user-defined samples (orbits, sizes and albedos) from the model.