Additive manufacturing of complex porous polymer geometries is a new field of advanced materials processing. Such new geometries can be used to fabricate porous polymer monoliths serving as a support for other material functions. Here, a novel fabrication technology to manufacture tailored 3D porous monoliths via additive manufacturing and templating is presented. The method is based on replicating a 3D-printed mold with a polymer solution of polyvinylidenfluorid-triethyl phosphate (PVDF-TEP) and induce phase separation of the polymer solution subsequently. In a second step, the mold is removed without affecting the porous PVDF phase. As a result, porous monoliths with a templated 3D architecture are successfully fabricated. The manufacturing process is successfully applied to complex structures and can be applied to any conceivable geometry. Coating the porous 3D monoliths with another PVDF solution allows applying a skin layer yielding an asymmetric membrane monolith. As a showcase, a polydimethylsiloxane coating even leads to a smooth and dense layer of micrometer size. The methodology enables a new generation of complex porous polymer monoliths with tailored surface coatings. For the combination of poly(dimethylsiloxane) on a porous support, gas/liquid mass transfer is used in blood oxygenation with reduced diffusion limitation is within reach.