Since the phrase is used to imply that there may be hidden problems (and God isn't generally associated with springing nasty surprises on people) only the reference to the Devil is meaningful.
This is a long running dispute between myself and my husband (obivoulsy I am correct and say Devil) but I have hear other people say God is in the detail.
"God is in the details" is a quote from Mies van der Rohe, the German architect, published in the New York Herald Tribune in 1969. However, there is a suggestion that it may also be attributed to Flaubert, the French poet, from rather earlier. I suspect the 'devil' version may just have been a later take-off of the 'God' one.
It sounds as if your husband may well be in the right!