This paper deals with the reconstruction of a 3-D spatio-spectral object observed by a multispectral imaging system, where the original object is blurred with a spectral-variant PSF (Point Spread Function) and integrated over few broad spectral bands. In order to tackle this ill-posed problem, we propose a multispectral forward model that accounts for direct (or auto) channels and between (or cross) channels degradation, by modeling the imaging system response and the spectral distribution of the object with a piecewise linear function. Reconstruction based on regularization methods is proposed, by enforcing spatial and spectral smoothness of the object. We test our approach on simulated data of the Mid-InfraRed Instrument (MIRI) Imager of the James Webb Space Telescope (JWST). Results on simulated multispectral data show a significant improvement over the conventional multichannel method.