The matching of competences, such as skills, occupations or knowledges, is a key desiderata for candidates to be fit for jobs. Automatic extraction of competences from CVs and Jobs can greatly promote recruiters' productivity in locating relevant candidates for job vacancies. This work presents the first model that jointly extracts and classifies competence from Danish job postings. Different from existing works on skill extraction and skill classification, our model is trained on a large volume of annotated Danish corpora and is capable of extracting a wide range of Danish competences, including skills, occupations and knowledges of different categories. More importantly, as a single BERT-like architecture for joint extraction and classification, our model is lightweight and efficient at inference. On a real-scenario job matching dataset, our model beats the state-of-the-art models in the overall performance of Danish competence extraction and classification, and saves over 50% time at inference.