Context. The Class 0 protostellar binary IRAS 16293-2422 is an interesting target for (sub)millimeter observations due to, both, the rich chemistry toward the two main components of the binary and its complex morphology. Its proximity to Earth allows the study of its physical and chemical structure on solar system scales using high angular resolution observations. Such data reveal a complex morphology that cannot be accounted for in traditional, spherical 1D models of the envelope. Aims. The purpose of this paper is to study the environment of the two components of the binary through 3D radiative transfer modeling and to compare with data from the Atacama Large Millimeter/submillimeter Array. Such comparisons can be used to constrain the protoplanetary disk structures, the luminosities of the two components of the binary and the chemistry of simple species. Methods. We present 13CO, C17O and C18O J=3-2 observations from the ALMA Protostellar Interferometric Line Survey (PILS), together with a qualitative study of the dust and gas density distribution of IRAS 16293-2422. A 3D dust and gas model including disks and a dust filament between the two protostars is constructed which qualitatively reproduces the dust continuum and gas line emission. Results and conclusions. Radiative transfer modeling of source A and B, with the density solution of an infalling, rotating collapse or a protoplanetary disk model, can match the constraints for the disk-like emission around source A and B from the observed dust continuum and CO isotopologue gas emission. If a protoplanetary disk model is used around source B, it has to have an unusually high scale-height in order to reach the dust continuum peak emission value, while fulfilling the other observational constraints. Our 3D model requires source A to be much more luminous than source B; LA ~ 18 $L_odot$ and LB ~ 3 $L_odot$.
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