The estimation of the residual background due to cosmic ray-induced air showers represents a key element of every analysis of Imaging Atmospheric Cherenkov Telescope (IACT) data. In the past, most techniques have relied on a measurement of the background in supposedly source-free regions within the observed field of view. However, this approach is problematic in regions with many (potentially overlapping) $\gamma$-ray sources or large-scale diffuse $\gamma$-ray emission, like e.g. the Galactic Plane. For these cases, a template-based 3D likelihood analysis might be superior. In this approach, a spectro-morphological model template, consisting of one or multiple source components and a background component, is fit to the data, resulting in a complete spectral and spatial description of the field of view. In this contribution, we present our efforts to establish a 3D likelihood analysis for data taken with the H.E.S.S. system of IACTs, using the open-source analysis packages ctools and Gammapy. In particular, we focus on the development of a template model for the cosmic ray-induced background - a major challenge in such an approach - from archival H.E.S.S. data. We characterise the obtained model and demonstrate its application using publicly available H.E.S.S. data. The validation of this analysis approach on experimental data also constitutes an important step towards the analysis of data from the upcoming Cherenkov Telescope Array (CTA).