1. H stood for Haploid since Jesus has no human father.
2. It recalls the H in the IHS logo emblazoned on much Christian paraphernalia. IHS dates from the earliest years of Christianity, being an abbreviation of "Jesus" in classical Greek characters. The Greek pronunciation is "Iesous," with the E sound being represented by the character eta, which looks like an H. When the symbol passed to Christian Romans, for whom an H was an H, the unaccountable character eventually became accepted as Jesus's middle initial.
3. H derives from the taunting Latin inscription INRH that was supposedly tacked on the cross by Roman soldiers: Iesus Nazarenus, Rex Hebrei (Jesus the Nazarene, King of the Hebrews). Trouble is, the inscription is usually given as INRI: Iesus Nazarenus, Rex Iudaeorum (J.C., King of the Jews).
Jesus H. Christ is an expression just as "Jesus Christ" Only with an H added in, most likely for humor.
Luke: Jesus H Christ! Praise your Grandpa! Are you here to die for our sins like your old man? Hey what does the H stand for?
Jesus H Christ: Henry
Luke: Jesus H Christ! Turn some water to wine! Let's party!
Jesus H Christ: hallelujah! Your prayers have been heard! Bring out the water!
Mary: Jesus H Christ! You'r to young to drink.
Jesus H Christ: My Grandpa damn you!
Luke: Jesus H Christ!, you said it.
and so on
Note: The phrase is no more-or-less blasphemous than "Jesus Christ"