Despite the application of state-of-the-art fully Convolutional Neural Networks (CNNs) for semantic segmentation of very high-resolution optical imagery, their capacity has not yet been thoroughly examined for the classification of Synthetic Aperture Radar (SAR) images. The presence of speckle noise, the absence of efficient feature expression, and the limited availability of labelled SAR samples have hindered the application of the state-of-the-art CNNs for the classification of SAR imagery. This is of great concern for mapping complex land cover ecosystems, such as wetlands, where backscattering/spectrally similar signatures of land cover units further complicate the matter. Accordingly, we propose a new Fully Convolutional Network (FCN) architecture that can be trained in an end-to-end scheme and is specifically designed for the classification of wetland complexes using polarimetric SAR (PolSAR) imagery. The proposed architecture follows an encoder-decoder paradigm, wherein the input data are fed into a stack of convolutional filters (encoder) to extract high-level abstract features and a stack of transposed convolutional filters (decoder) to gradually up-sample the low resolution output to the spatial resolution of the original input image. The proposed network also benefits from recent advances in CNN designs, namely the addition of inception modules and skip connections with residual units. The former component improves multi-scale inference and enriches contextual information, while the latter contributes to the recovery of more detailed information and simplifies optimization. Moreover, an in-depth investigation of the learned features via opening the black box demonstrates that convolutional filters extract discriminative polarimetric features, thus mitigating the limitation of the feature engineering design in PolSAR image processing. Experimental results from full polarimetric RADARSAT-2 imagery illustrate that the proposed network outperforms the conventional random forest classifier and the state-of-the-art FCNs, such as FCN-32s, FCN-16s, FCN-8s, and SegNet, both visually and numerically for wetland mapping.