A method for making a polymeric microfluidic structure in which two or more components (layers) of the microfluidic structure are fixedly bonded or laminated with a weak solvent bonding agent, particularly acetonitrile or a mixture of acetonitrile and alcohol. In an aspect, acetonitrile can be used as a weak solvent bonding agent to enclose a microstructure fabricated in or on a non-elastomeric polymer such as polystyrene, polycarbonate, acrylic or other linear polymer to form a three-dimensional microfluidic network. The method involves the steps of wetting at least one of the opposing surfaces of the polymeric substrate components with the weak solvent bonding agent in a given, lower temperature range, adjacently contacting the opposing surfaces, and thermally activating the bonding agent at a higher temperature than the lower temperature range for a given period of time. The contacted polymeric substrates may also be aligned prior to thermal activation and compressed during thermal activation. A laminated, polymeric microfluidic structure is also disclosed.