We present a mid-infrared investigation of the scaling relations between supermassive black hole masses (MBH) and the structural parameters of the host spheroids in local galaxies. This work is based on 2D bulge-disc decompositions of Spitzer/IRAC 3.6 μm images of 57 galaxies with MBH estimates. We first verify the accuracy of our decomposition by examining the Fundamental Plane (FP) of spheroids at 3.6 μm. Our estimates of effective radii (Re) and average surface brightnesses, combined with velocity dispersions from the literature, define a FP relation consistent with previous determinations but doubling the observed range in Re. None of our galaxies is an outlier of the FP, demonstrating the accuracy of our bulge-disc decomposition which also allows us to independently identify pseudo-bulges in our sample. We calibrate M/L at 3.6 μm by using the tight Mdyn–Lbul relation (∼0.1 dex intrinsic dispersion) and find that no colour corrections are required to estimate the stellar mass. The 3.6 μm luminosity is thus the best tracer of stellar mass yet studied. We then explore the connection between MBH and bulge structural parameters (luminosity, mass, effective radius). We find tight correlations of MBH with both 3.6 μm bulge luminosity and dynamical mass (MBH/Mdyn∼ 1/1000), with intrinsic dispersions of ∼0.35 dex, similar to the MBH–σ relation. Our results are consistent with previous determinations at shorter wavelengths. By using our calibrated M/L, we rescale MBH–Lbul to obtain the MBH–M★ relation, which can be used as the local reference for high-z studies which probe the cosmic evolution of MBH–galaxy relations and where the stellar mass is inferred directly from luminosity measurements. The analysis of pseudo-bulges shows that four out of nine lie on the scaling relations within the observed scatter, while those with small MBH are significantly displaced. We explore the different origins for such behaviour while considering the possibility of nuclear morphological components not reproduced by our 2D decomposition.