Building segmentation in high-resolution InSAR images is a challenging task that can be useful for large-scale surveillance. Although complex-valued deep learning networks perform better than their real-valued counterparts for complex-valued SAR data, phase information is not retained throughout the network, which causes a loss of information. This paper proposes a Fully Complex-valued, Fully Convolutional Multi-feature Fusion Network(FC2MFN) for building semantic segmentation on InSAR images using a novel, fully complex-valued learning scheme. The network learns multi-scale features, performs multi-feature fusion, and has a complex-valued output. For the particularity of complex-valued InSAR data, a new complex-valued pooling layer is proposed that compares complex numbers considering their magnitude and phase. This helps the network retain the phase information even through the pooling layer. Experimental results on the simulated InSAR dataset show that FC2MFN achieves better results compared to other state-of-the-art methods in terms of segmentation performance and model complexity.