Multispectral (MS) images contain richer spectral information than RGB images due to their increased number of channels and are widely used for various applications. However, achieving accurate estimation in MS images remains challenging, as previous studies have struggled with spectral diversity and the inherent entanglement between the illuminant and surface reflectance spectra. To tackle these challenges, in this paper, we propose a novel Illumination spectrum estimation technique for MS images via Surface reflectance modeling and Spatial-spectral feature generation (ISS). The proposed technique employs a learnable spectral unmixing (SU) block to enhance surface reflectance modeling, which was unattempted in the illumination spectrum estimation, and a feature mixing block to fuse spectral and spatial features of MS images with cross-attention. The features are refined iteratively and processed through a decoder to produce an illumination spectrum estimator. Experimental results demonstrate that the proposed technique achieves state-of-the-art performance in illumination spectrum estimation in various MS image datasets. The code is available at https://github.com/heyjinnii/ISS-MSI.git.