P-type multiwalled carbon nanotubes (MWCNTs), as well as heterostructures fabricated by direct deposition of inorganic thermoelectric materials as antimony and bismuth chalcogenides on MWCNT networks are known as perspective materials for application in flexible thermoelectric polymer-based composites. In this work, the electrical response of three types of Sb2Te3-MWCNT heterostructures-based flexible films—free standing on a flexible substrate, encapsulated in polydimethylsiloxane (PDMS), and mixed in polyvinyl alcohol (PVA) is studied in comparison with the flexible films prepared by the same methods using bare MWCNTs. The electrical conductance of these films when each side of it was subsequently subjected to compressive and tensile stress during the film bending down to a 3 mm radius is investigated in relation to the distribution gradient of Sb2Te3-MWCNT heterostructures or bare MWCNTs within the film. It is found that all investigated Sb2Te3-MWCNT films exhibit a reversible increase in the conductance in response to the compressive stress of the film side with the highest filler concentration and its decrease in response to the tensile stress. In contrast, free-standing and encapsulated bare MWCNT networks with uniform distribution of nanotubes showed a decrease in the conductance irrelevant to the bending direction. In turn, the samples with the gradient distribution of the MWCNTs, prepared by mixing the MWCNTs with PVA, revealed behavior that is similar to the Sb2Te3-MWCNT heterostructures-based films. The analysis of the processes impacting the changes in the conductance of the Sb2Te3-MWCNT heterostructures and bare MWCNTs is performed. The proposed in this work bending method can be applied for the control of the uniformity of distribution of components in heterostructures and fillers in polymer-based composites.