It is actually called a Detached House.
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When one party controls the House and the other controls the Senate it is called divided government.
In the UK we would refer to a house that is not attached to another house as detached. Just two houses joined together are semi-detached and houses in a long row are called terraced houses (I believe they are referred to as row houses in the USA).
when one party controls the House and another party controls the Senate
unicameral A one house legislature is a unicameral. A two house legislature is a bicameral.
the middle house