Fourier transform infrared (FTIR) microspectroscopy images contain information from the whole infrared spectrum used for microspectroscopic analyses. In combination with the FTIR image, visible light images are used to depict the area from which the FTIR spectral image was sampled. These two images are traditionally acquired as separate files. This paper proposes a histogram shifting-based data hiding technique to embed visible light images in FTIR spectral images producing single entities. The primary objective is to improve data management efficiency. Secondary objectives are confidentiality, availability, and reliability. Since the integrity of biomedical data is vital, the proposed method applies reversible data hiding. After extraction of the embedded data, the FTIR image is reversed to its original state. Furthermore, the proposed method applies authentication tags generated with keyed Hash-Based Message Authentication Codes (HMAC) to detect tampered or corrupted areas of FTIR images. The experimental results show that the FTIR spectral images carrying the payload maintain good perceptual fidelity and the payload can be reliably recovered even after bit flipping or cropping attacks. It has been also shown that extraction successfully removes all modifications caused by the payload. Finally, authentication tags successfully indicated tampered FTIR image areas.