Yes it is! Greenland left the European Union in 1985, while Denmark remained inside the EU. Since half-a-country cannot be an EU member, the only way that is possible is if they are both countries! (There is the Kingdom of Denmark, a supra-national entity, as well as the Country of Denmark, which is one of the constituent countries of the Kingdom. The other countries that are part of the Kingdom are Greenland and Faroe Islands).
It is a country, for similar reasons that relate to Greenland above. (Next time they play a football international in the European Championship be sure to stand outside with your sign objecting!). This article explains more fully.