This is a comprehensive study of the effect of strong magnetic fields on superconductivity in PbTe/PbS heterostructures with semiconducting layers of different thicknesses. Metallic conductivity and superconductivity (critical temperature T c 6.5 K) in PbTe/PbS heterostructures are caused by inversion of bands along a continuous network of misfit dislocations that develops at the interfaces between semiconductor layers of sufficient thickness (d > 80 nm). With decreasing d the continuity of the superconducting interface is disrupted, T c decreases, and the metallic conductivity changes to a semiconducting type. Disruption of the continuity of the superconducting interface is found to be a necessary condition for observing a magnetic-field induced superconductor-insulator transition (SIT) and has a significant influence on its features: a fan-like set of resistance curves R(T); intersection of the R(B) curves for fields perpendicular, as well as parallel, to the interface; and, negative magnetoresistance. A scaling analysis based on Fisher's theoretical model is carried out for these samples. No evidence of a SIT was observed in heterostructures with a perfect interface. It appears that the SIT effect is related to percolation phenomena characteristic of granular superconductors. V C 2013 AIP Publishing LLC.