He was born in Kragerø, Norway as the son of merchant and politician Johan Christian Heuch (1794–1843) and his wife Christine Elisabeth Bonnevie (1803–1863).[1]His paternal grandfather Peter Andreas Heuch (1756–1825) was among the wealthiest persons in Southern Norway.[2] On the maternal side he was a great-grandson of Honoratus Bonnevie and a first cousin of Jacob Aall Bonnevie;[1] the latter was the father of zoologist Kristine Elisabeth Heuch Bonnevie.[3]
In December 1861, he married Kirsten Anna Janette Elieson (1839–1913), a daughter of jurist and politician John Collett Postumus Elieson.[1] Their daughter Kristine Elisabeth married barrister Fredrik Moltke Bugge.[4] Other direct descendants of J. C. Heuch include ceramicist Hanne Heuch.[2]