Purpose - The work is aimed at studying the electromagnetic interaction between a homogeneous, isotropic single-negative (SNG) slab and an inhomogeneous, anisotropic double-positive (DPS) slab. Design/methodology/approach - The approach is based on the transformation optics framework, which allows systematic design and modelling of anisotropic, inhomogeneous metamaterials with inherent field-manipulation capabilities. Findings - The paper finds that a transformation-optics-based DPS slab can compensate the inherent opaqueness to the electromagnetic radiation of a SNG slab. Here, ``compensation’’ means that the resulting bi-layer may give rise to zero-reflection for a normally-incident plane wave at a given frequency. Such phenomenon is inherently accompanied by (de)funneling effects for collimated-beam illumination, and it turns out to be quite robust to material losses as well as geometrical and constitutive-parameter truncation. Originality/value - The results provide further evidence and insight in how SNG-like responses may be emulated (within narrow parametric ranges) by suitably-engineered spatial inhomogeneity and anisotropy in DPS media. Moreover, they also show that resonant transmission phenomena through SNG materials may be engineered via the powerful framework of transformation optics.