While the photocatalytic degradation of dyes and other pollutants from wastewater by titanium dioxide (TiO2) is recognized as a highly efficient process, the cost of using UV radiation still prevents it from large-scale application. One method of moving from the UV activation energy towards the visible (Vis) spectral range could be the use of n-p heterostructures, with an overall band gap lower than that of TiO2. In this paper, thin film heterostructures based on TiO2 as n-type semiconductor and copper zinc tin sulfide (Cu2ZnSnS4, CZTS) as p-type semiconductor were tested in the dye removal of methylene blue, under Vis and solar simulated radiation. The thickness of the outer, TiO2 layer was varied by changing the precursor concentration (TiCl4, 0.05 M and 0.1 M). It was found that a higher titania film thickness promotes enhanced crystallinity, which is useful in a photocatalyst. From a morphological point of view, both samples showed a continuous coverage of the CZTS thin film, with multiple TiO2 aggregates on the heterostructure surface. The sample containing TiO2 prepared from the 0.05 M solution, exhibits Cu-poor, Zn-rich composition which promotes a better charge carrier transport in the material. This is confirmed by the higher dye removal efficiency (27.6%) of this sample, under Vis irradiation, for 8 h. The addition of 3% UV to the Vis radiation (simulated solar radiation) leads to a further increase of nearly 7.7% in the dye removal efficiency.