In an intimate interview, Justin Welby said he was "very careful" around booze but he regularly frets about whether struggles with alcohol dependency run in his family.
Speaking with the Sunday Times Magazine, the Anglican leader said: "I frequently worry about having my parents' addictions.
"My wife Caroline and I are extremely honest with each other, and I'm very careful about my drinking."
Archbishop Justin, who discovered last year that the man who helped raised him was not in fact his birth father, also expressed his "regret" at "not knowing" Sir Anthony Montague, his biological dad.
The 61-year-old also described the divorce of his mother Jane Portal and father Gavin Welby when he was three-years-old as "unpleasant", saying he lived through a "noisy, disturbed children".
He went on to say: "I've often asked myself if my experience of childhood shaped my parenting.
"One never knew what was going on with my father... I've tried to be more transparent."
Archbishop Justin also shared how he enjoys being "a family man" when his church duties on Christmas day are over and he can sit down to dinner.
In October, he publicly acknowledged for the first time a battle with depressive episodes - describing to Alistair Campbell at GQ magazine moments of feeling hopeless.