Parisi has four children; Mandy (born 1981), Dean (born 1987) were born from previous relationships. On 14 July 2009 Parisi announced that he and his girlfriend, BBC Producer Tara Wyer, were expecting a baby together. Tara gave birth to Cliff's fourth child, a son named Arthur, on 28 December 2009. The couple first met in February 2009 before formally beginning a relationship in April and, since discovering the pregnancy, lived together in Parisi's home in Highgate, North London and plan to marry.
After finishing the former TV series, Parisi auditioned for what would be his most famous role: Minty Peterson in EastEnders. He was recommended for the part by close friend and EastEnders actor Steve McFadden. Since his inception into the soap opera in 2002 the public have seen his character Minty form a close friendship with Garry Hobbs (Ricky Groves) and evolve from a cold-hearted landlord to a hapless unlucky-in-love mechanic and then to finding love with established characters Heather Trott (Cheryl Fergison) and Manda Best (Josie Lawrence). He made his final appearance on 21 September 2010, ending eight years on the show.
Since 2012, Parisi has starred in the BBC period drama Call the Midwife, appearing as Fred.
