We propose a new interior region-of-interest (ROI) image reconstruction method for computed tomography. The additional information to make the interior problem uniquely solvable is that a specific region inside the interior ROI is known to have uniform intensity level, but the constant level is unknown. The uniqueness of solution in this situation is analyzed by combining two existing approaches, namely (1) when the full knowledge of a small region inside the interior ROI is known, and (2) when the complete interior ROI is piecewise constant. The image reconstruction is provided by a mixed region and voxel based Poisson likelihood ML-EM algorithm that takes care of the photon statistics in emission tomography. This algorithm reconstructs the unknown constant (region-model) and the rest of the interior ROI (voxel-model) simultaneously. The uniqueness result assumes that all line integrals through the interior ROI are acquired. When only finite number of projection views are available, the mixed region and voxel based ML-EM algorithm can also reduce image artifacts from sparse-view and interior data acquisition in stationary multipinhole SPECT.