  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 $L_\odot$.
