The field of human cell research is rapidly changing due to the introduction of microphysiological systems (MPSs), which commonly feature two stacked microchannels separated by a porous membrane for in-vitro barrier modeling. An essential component to adequately representing a subset of human organ or tissue functions in these microfluidic systems is the concentration distribution of the bio-species involved. In particular, when different cell types are cultured, a delicate balance between media mixing and cellular signaling is required for long-term maintenance of the cellular co-culture. In this work, we experimentally measured the effects of various control parameters on the transient and steady average molecular concentration at the bilayer device outlet. Using these experimental results for validation, we then numerically investigated the concentration distributions due to the convection-diffusion mass transport in both microchannels. The effects of media flow rate, separation membrane porosity, molecular size, microchannel dimensions and flow direction have been systematically characterized. The transient response is found to be negligible for cell co-cultures lasting several days, while the steady-state concentration distribution is dominated by the media flow rate and separation membrane porosity. Numerically computed concentration profiles reveal self-similarity characteristics featuring a diffusive boundary layer, which can be manipulated for successful maintenance of cell co-culture with limited media mixing and enhanced cell signaling.