This paper presents an acquisition system and a procedure to capture 3D scenes in different spectral bands. The acquisition system is formed by a monochrome camera, and a Liquid Crystal Tunable Filter (LCTF) that allows to acquire images at different spectral bands in the [480, 680]nm wavelength interval. The Synthetic Aperture Integral Imaging acquisition technique is used to obtain the elemental images for each wavelength. These elemental images are used to computationally obtain the reconstruction planes of the 3D scene at different depth planes. The 3D profile of the acquired scene is also obtained using a minimization of the variance of the contribution of the elemental images at each image pixel. Experimental results show the viability to recover the 3D multispectral information of the scene. Integration of 3D and multispectral information could have important benefits in different areas, including skin cancer detection, remote sensing and pattern recognition, among others.