Organ-on-chip (OoC) technology is increasingly used for biomedical research and to speed up the process of bringing a drug from lab to the market. The main fluidic components of an OoC device are microfluidic channels and porous membranes arranged in three dimensions. Current chips are often assembled from several parts. In the development phase a small change in design will cause a delay in the research because a new prototype has to be built and assembled again step-by-step. The research discussed in this paper addresses this point by targeting a monolithic 3D device that can be fabricated in a single lithography and development step, enabling rapid prototyping. Two-photon lithography (TPL) was used in combination with a positive photoresist AZ 4562. The exposure process was characterized, which included an experimental and theoretical study of the voxel size and shape. It was found that the voxel has an hourglass-shape for the laser power settings that were required for process stability. The smallest pores we could produce with these settings measured 250 nm in diameter. The TPL process was then used to fabricate a microfluidic device featuring two crossed channels each one on a separate height-level, connected by a membrane in the centre. Access to the channels was provided through 4 reservoirs from the top-side of the device. The device was successfully filled with water and dried to see whether it can withstand the corresponding capillary forces.