I think "babe" is totally in character for Jimmy. I've got a feeling he even called one of his girlfriends that on the show - but don't quote me on it...
Superman: Why is it that good villains never die? Batman: Clark, what the hell are good villains? => Superman/Batman: Public Enemies
Hmm... I think what Jimmy might say about a woman and to a woman might be different. I don't think he'd call a woman he just met 'babe'. But I think he'd get all soft and mushy around his girlfriend and might call her baby.