For over a quarter of a century, the EU and the Council of Europe have worked together for the consolidation of multilateralism across the world, the upholding of democratic institutions and values, the protection of human rights and fundamental liberties and the strenghtening of the rule of law. Their cooperation in these areas has mainly materialized in the form of solid inter-institutional instruments providing for highly-specialized technical, institutional and networking support: the joint programmes. The EU is in charge of most of the funding to the joint programmes while the Council of Europe is responsible for their enforcement.
You can find a full list of joint programmes here. Currently, over 50 joint programmes are in operation, with a cumulative budget of over €200M. Programmes are mainly in the fields of rule of law and human rights and generally cover the Western Balkans, Turkey, the Eastern Partnership and the Southern Mediterranean.