The palace and its interior with valuable cabinets from the studio of Abraham and David Roentgen, paintings and a large collection of Wedgwood porcelain were open to the public. So it is today after a long period of restorations. 

Duchess Louise had her private home in the adjacent "Grey House", which can be visited today too.

It is part of the Dessau-Wörlitz Realm, a UNESCO Heritage site, one of the first and largest English parks in Germany and continental Europe.  Laid out between 1765 and 1817, it forms part of a collective project covering a 25km area, including five sections: (1) the Schloss Garten with its Englischer Sitz, modelled on Stourhead but intended as a private garden; (2) the Neumark Garten with a canal, islands, a circular building modelled on Stowe; (3) the Schloss Garten with a Gothic House, a Temple of Venus and a Temple of Flora; (4) the garden on the north-east shore of the lake; (5) the New Gardens with mementos of Italy. 

For more detailed information see website.