  The interface between topological and normal insulators hosts metallic states
that appear due to the change in band topology. While these topological states
at a surface, i.e., a topological insulator-air/vacuum interface, have been
studied intensely, topological states at a solid-solid interface have been less
explored. Here we combine experiment and theory to study such \textit{embedded}
topological states (ETSs) in heterostructures of GeTe (normal insulator) and
Sb$_2$Te$_3$ (topological insulator). We analyse their dependence on the
interface and their confinement characteristics. To characterise the
heterostructures, we evaluate the GeTe-Sb$_2$Te$_3$ band offset using X-ray
photoemission spectroscopy, and chart the elemental composition using atom
probe tomography. We then use first-principles to independently calculate the
band offset and also parametrise the band structure within a four-band
continuum model. Our analysis reveals, strikingly, that under realistic
conditions, the interfacial topological modes are delocalised over many lattice
spacings. Interestingly, the first-principles calculations indicate that the
ETSs are relatively robust to disorder and this may have practical
ramifications. Our study provides insights into how to manipulate topological
modes in heterostructures and also provides a basis for recent experimental
findings [Nguyen \textit{et al.}, Sci. Rep. \textbf{6}, 27716 (2016)] where
ETSs were seen to couple over large distances.
