Stephen is a local - he lives in Largs Bay with his wife Antonia and sons Benjamin and Isaac, where his father and his family are from.  He spent much of his childhood at Alberton Oval watching the Magpies, at the beach at Largs, or fishing off North Haven. When it came time to buy his home, he only wanted to live in Largs.

Mr Mullighan was first elected as the Member for Lee in the South Australian Parliament in 2014.

Mr Mullighan took up his position as Minister for Transport & Infrastructure, Minister Assisting the Minister for Planning, Minister Assisting the Minister for Housing and Urban Development on 26 March 2014.

In 2016, Mr Mullighan was appointed the Minister for Housing and Urban Development.

Prior to his appointment as Minister, Mr Mullighan led Deloitte's economics team in Adelaide between 2010-2013, providing economic advice to corporate clients, non-profit sector and state and federal governments.

He served as the Deputy Chief of Staff to the South Australian Premier and Treasurer, Hon Jay Weatherill MP, from 2013 to 2014. During this time Mr Mullighan was responsible for several key policy areas including budget development, taxation policy, investment strategy and State-Commonwealth financial relations.

He holds a Bachelor of Arts degree from the University of Adelaide.

Mr Mullighan was returned as the Member for Lee at the 2018 South Australian Election.

Our community is one of the best in Adelaide and not just because of its beautiful beaches, proud industrial and maritime heritage, tourism attractions and successful sporting clubs. Our community is such a great part of South Australia because of its people. Residents of the Lefevre Peninsula and the western suburbs truly are the best going around: neighbourly, compassionate, proud of their heritage and always looking out for those in our community who need a hand. To be considered a worthy representative to this place is a great honour, indeed. Deputy Speaker, I can assure you that I will be working conscientiously to do my best on their behalf.
— Maiden Speech 7 May 2014