I really wish there was a consensus on how to spell "Jeeze"
I usally spell it as "Geez," seeing as how that's the most accepted form of the utterance (since it's not really a word) in most printed materials, i.e. comics. However, the spelling of "Geez," to a non-native speaker unfamiliar with the term might have the same pronounciation as it does in the word "geezer." Still, other examples of the former pronounciation can be found in "Gee," as in "gee whiz," and to a lesser extent in the word "geese."
However, the utterance "geez/jeez/jeeze" could very well have been a euphemized way of exclaiming "Jesus!" if you were into the whole not-taking-the-Lord's-name-in-vain thing (which is not completely accurate according to the original language of the Commandment). If this is indeed the case, then the spelling should be "jeez," end of story; however, the case remains that both spellings for this word that's not a word are in use.