Data fusion of different imaging techniques allows a comprehensive description of chemical and biological systems. Yet, joining images acquired with different spectroscopic platforms is complex because of the different sample orientation and image spatial resolution. Whereas matching sample orientation is often solved by performing suitable affine transformations of rotation, translation, and scaling among images, the main difficulty in image fusion is preserving the spatial detail of the highest spatial resolution image during multitechnique image analysis. In this work, a special variant of the unmixing algorithm Multivariate Curve Resolution Alternating Least Squares (MCR-ALS) for incomplete multisets is proposed to provide a solution for this kind of problem. This algorithm allows analyzing simultaneously images collected with different spectroscopic platforms without losing spatial resolution and ensuring spatial coherence among the images treated. The incomplete multiset structure concatenates images of the two platforms at the lowest spatial resolution with the image acquired with the highest spatial resolution. As a result, the constituents of the sample analyzed are defined by a single set of distribution maps, common to all platforms used and with the highest spatial resolution, and their related extended spectral signatures, covering the signals provided by each of the fused techniques. We demonstrate the potential of the new variant of MCR-ALS for multitechnique analysis on three case studies: (i) a model example of MIR and Raman images of pharmaceutical mixture, (ii) FT-IR and Raman images of palatine tonsil tissue, and (iii) mass spectrometry and Raman images of bean tissue.