We present a novel 3D hybrid assembly of a polymer microfluidic chip with polycarbonate track-etched membrane (PCTEM) enabling membrane-supported cell culture. Two chip designs have been developed to establish either diffusive or convective reagent delivery using the integrated PCTEM. While it is well suited to a range of cell-based assays, we specifically employ this platform for the screening of a common antitumor chemotoxic agent (mitomycin C – MMC) on the HL60 myeloid leukemia cell line. The toxic activity of MMC is based on the generation of severe DNA damage in the cells. Using either mode of operation, the HL60 cells were cultured on-chip before, during, and after exposure to MMC at concentrations ranging from 0 to 50 μM. Cell viability was analysed off-chip by the trypan blue dye exclusion assay. The results of the on-chip viability assay were found to be consistent with those obtained off-chip and indicated ca. 40% cell survival at MMC concentration of 50 μM. The catalogue of capabilities of the here described cell assay platform comprises of (i) the culturing of cells either under shear-free conditions or under induced through-membrane flows, (ii) the tight time control of the reagent exposure, (iii) the straightforward assembly of devices, (iv) the flexibility on the choice of the membrane, and, prospectively, (v) the amenability for large-scale parallelization.