Abstract The Messenger Interface Monte Carlo Mappings V (M 3 ) is a photoionization code adopting the fully self-consistent Monte Carlo radiative transfer (MCRT) technique, which presents a major advance over previous photoionization models with simple geometries. M 3 is designed for modeling nebulae in arbitrary three-dimensional geometries. In this paper, we describe the MCRT technique and the microphysics implemented in M 3 , including photoionization, collisional ionization, free–free and free–bound recombination, and two-photon radiation. We put M 3 through the Lexington/Meudon benchmarks to test the reliability of the new code. We apply M 3 to three H ii region models with fiducial geometries, demonstrating that M 3 is capable of dealing with nebulae with complex geometries. M 3 is a promising tool for understanding emission-line behavior in the era of SDSS-V/LVM and James Webb Space Telescope, which will provide high-quality data of spatially resolved nearby H ii regions and highly turbulent local and high-redshift H ii regions.