The demand for novel green ways of fabricating high-performance polymer foams is increasing due to the wide application area. Especially in the field of membrane technology, processing techniques such as foam extrusion of diblock copolymers are of high interest. Consequently, it is necessary to reveal information about the thermal and rheological properties of diblock copolymers in order to fine-tune the optimum processing parameters because of their different behaviour compared to homopolymers. This study focuses on the thermal properties and rheological behaviour of polystyrene-block-poly(4-vinylpyridine) diblock copolymers. Besides the investigation of the influence of processing parameters on the foam structure, morphological aspects are considered as well. Here, the technique of batch foaming is applied with carbon dioxide (CO2) as blowing agent with foaming temperatures between 90 120 °C. Using high pressure differential scanning calorimetry, the plasticising effect of CO2 is confirmed by a decrease of the glass transition temperature of the polystyrene and the poly(4-vinylpyridine) domains at elevated pressures. Furthermore, rheological experiments in the oscillatory mode were performed in order to elucidate the influence of composition and molecular weight on the viscoelastic properties. A plateau of the storage and the loss modulus at low frequencies appears because of the microphase-separated morphology. Experiments with a constant shear rate show that the steady-state viscosity is characterised by a pronounced structure viscous behaviour. Finally, the analysis of the foamed diblock copolymers reveals that the foam density decreases with molecular weight of the diblock copolymers for the chosen processing parameters. Optimum foaming temperature with regard to the foam structure is 110 °C at which the foam cells are regularly distributed.