Skin　lesions　and　thyroid　cancer　have　become　diseases　with　a　high　incidence.　The　computer-aided　diagnosis　(CAD)　system　for　dermatological　diseases　offers　one　of　the　most　remarkable　performance　where　deep　learning　technologies　demonstrate　their　superiority　in　surpassing　human　experts.　For　developing　a　CAD　system,　a　critical　step　is　skin　lesions　and　thyroid　nodules　diagnosis　from　dermoscopic　images　and　ultrasound　images,　respectively.　Although　notable　successes　have　been　obtained　using　deep　convolutional　neural　network　(DCNN)　models,　several　challenges　hamper　the　practical　applications　in　clinical　due　to　the　complexity　of　clinical　data,　e.g.,　skin　lesions　or　thyroid　nodules　are　irregular　shapes　or　low　contrast.　To　alleviate　these　issues,　we　propose　a　novel　dual　encoder-decoder　network,　called　H-Net,　for　automated　thyroid　nodule　and　skin　lesion　segmentation.　Specifically,　a　shallow　CNN　is　applied　at　its　left　to　learn　the　low-level　details　information　called　L-Net　and　a　deep　CNN　is　employed　at　its　right　to　capture　the　high-level　information　called　R-Net.　Furthermore,　to　transfer　information　between　the　L-Net　and　the　R-Net　mutually,　we　propose　a　novel　crossed　skip　connection　strategy,　which　is　a　specific　reliability　skip　connection　way.　In　addition,　to　enhance　the　representation　learning　ability　of　the　proposed　pipeline,　we　propose　a　novel　contextual　information　encoding　module,　which　replaces　conventional　convolutional　layers　in　H-Net.　Meanwhile,　we　propose　a　novel　hybrid　loss　to　alleviate　the　imbalance　training　problem.　To　validate　the　effectiveness　of　H-Net,　600　pairs　of　dermoscopic　images　and　139　pairs　of　ultrasound　images　have　been　used　for　evaluation　in　experiments.　Seven　latest　biomedical　image　segmentation　approaches　are　compared,　and　ten　metrics　are　utilized　to　evaluate　the　segmentation　performance.　Extensive　experimental　results　demonstrate　that　our　H-Net　yields　the　new　record,　achieving　a　mIoU　value　of　84.8%　on　the　ISIC-2017　dataset　and　a　mIoU　value　of　87.5%　on　the　TNUI-2021　dataset,　which　outperforms　state-of-the-art　approaches　in　both　visual　comparisons　and　quantitative　evaluation.　The　codes　are　available　at　https://github.com/zxg3017/H-Net.　©　2022　Elsevier　Inc.