Hyperspectral Image (HSI) unmixing is a critical problem in remote sensing image processing. It aims to estimate the pure spectral signatures and their fractional abundances in each HSI pixel. Generally, most spectral-spatial unmixing methods do not exploit the contextual structure of HSI data cube. Therefore, in order to fully utilize the spatial information, we propose a new approach for spectral-spatial unmixing based on deep learning and Extended Morphological Profiles (EMPs). First, a latent representation from the original HSI data (spectral features) and the morphological profiles (spatial features) is obtained through the AutoEncoder (AE) network. Then, the estimation of both endmembers and abundance maps is achieved by the Convolutional AE (CAE). Experiments are performed using two HSI benchmarks which are Jasper Ridge and Samson. Compared to a spectral-spatial unmixing method, our proposed method shows significantly higher performance.