Question: Which two units of government jointly share a ministerial position formerly held by the conservative MP from Hemel Hempstead?

Context paragraphs:
Hemel Hempstead by-election, 1937: The Hemel Hempstead by-election of 1937 was held on 22 June 1937.  The by-election was held due to the elevation to the peerage of the incumbent Conservative MP, John Davidson.  It was won by the Conservative candidate Frances Davidson.

Hemel Hempstead railway station: Hemel Hempstead railway station is on the West Coast Main Line, on the western edge of the town of Hemel Hempstead, Hertfordshire, England.  The station is 24+1/2 mi north-west of London Euston on the West Coast Main Line.  Hemel Hempstead is managed by London Midland and all train services are operated by London Midland and Southern.

Hemel Hempstead Swimming Club: Hemel Hempstead Swimming Club is a swimming club based in Hemel Hempstead, Hertfordshire, United Kingdom and was established in 1913.  Hemel Hempstead Swimming Club (HHSC) ranks as one of Hertfordshire's premier clubs.  The Club has in excess of 220 members from age 5 to Masters Level and their swimmers compete regularly in a wide range of competitions.

Gadebridge: Gadebridge is a district of Hemel Hempstead in Hertfordshire, UK, located north west of Hemel Hempstead old town.  It was developed from land that once formed part of Gadebridge House in the 1960s and centres on the Rossgate shopping parade.  Gadebridge Park is the largest green space in Hemel Hempstead.  A major Roman villa was discovered here at the time of its development (Gadebridge Park Roman Villa).  The population of the Dacorum ward (including Piccotts End) at the 2011 Census was 5,655.

Hemel Storm: The Hemel Storm are a basketball team currently competing in Division 1 of the English National Basketball League.  The team is based in Hemel Hempstead, Hertfordshire and play their home games in the Hemel Hempstead Sportspace facility.  Over their short history, the club has been based in several locations across Hertfordshire and North London, before settling into their current, long-term home in 2010.

Leader of the House of Commons: The Leader of the House of Commons is generally a member of the Cabinet of the United Kingdom who is responsible for arranging government business in the House of Commons.  However, the current incumbent, Andrea Leadsom, is not a member of the cabinet but does attend cabinet meetings.  This office does not attract a ministerial salary, and as such it is usually held jointly with another ministerial position (often a sinecure).  Historically, the position was usually held by the Prime Minister if they sat in the House of Commons; in more recent years, the post has been held jointly with that of Lord President of the Council, Lord Privy Seal, or First Secretary of State.

Mike Penning: Michael Alan Penning (born 28 September 1957) is a British Conservative Party politician, who has served as Member of Parliament for Hemel Hempstead since 2005.

Nash Mills: Nash Mills is a civil parish within Hemel Hempstead and Dacorum Borough Council on the northern side of the Grand Union Canal, formerly the River Gade, and in the southernmost corner of Hemel Hempstead.  It takes its name from the mill owned by John Dickinson in the 19th century (Nash Mill).

Minister for Policing: The Minister of State for Policing, Fire and Criminal Justice is a ministerial position held jointly at the Home Office and the Ministry of Justice in the Government of the United Kingdom.  Conservative MP Mike Penning held the portfolio between July 2014 and July 2016.  He was promoted by new Prime Minister Theresa May in 2016, with his successor announced as Brandon Lewis.  The post was created by the splitting of the now-defunct office of the Minister for Security, Counter-Terrorism, Crime and Policing into two new ministerial posts: Security & Counter-Terrorism and Crime & Policing.  From January 2016 onwards the Minister is responsible for the portfolio for Fire and Rescue Services.

Hemel Hempstead by-election, 1920: The Hemel Hempstead by-election of 1920 was held on 9 November 1920.  The by-election was held due to the death of the incumbent Coalition Conservative MP, Gustavus Talbot.  It was won by the Coalition Conservative candidate John Davidson, who was elected unopposed.

Supporting paragraphs: Minister for Policing Mike Penning
Answer: Home Office and the Ministry of Justice