Electrical impedance tomography (EIT) is widely used for bedside monitoring of lung ventilation status. Its goal is to reflect the internal conductivity changes and estimate the electrical properties of the tissues in the thorax. However, poor spatial resolution affects EIT image reconstruction to the extent that the heart and lung-related impedance images are barely distinguishable. Several studies have attempted to tackle this problem, and approaches based on decomposition of EIT images using linear transformations have been developed, and recently, U-Net has become a prominent architecture for semantic segmentation. In this paper, we propose a novel semi-Siamese U-Net specifically tailored for EIT application. It is based on the state-of-the-art U-Net, whose structure is modified and extended, forming shared encoder with parallel decoders and has multi-task weighted losses added to adapt to the individual separation tasks. The trained semi-Siamese U-Net model was evaluated with a test dataset, and the results were compared with those of the classical U-Net in terms of Dice similarity coefficient and mean absolute error. Results showed that compared with the classical U-Net, semi-Siamese U-Net exhibited performance improvements of 11.37% and 3.2% in Dice similarity coefficient, and 3.16% and 5.54% in mean absolute error, in terms of heart and lung-impedance image separation, respectively.