Balthazar's dad is a somewhat anonymous member of Master Payne's Circus of Adventure. His name is never given in the comic, but according to the print novel Agatha H. and the Clockwork Princess, it's Guntar. He also seems fairly shy, as far as appearances go; it looks like the first time we see him is , long after he's first been mentioned, although there's some chance that he's in the background on some earlier occasion.
We learn a little about him by way of Balthazar's description of his clank and personal surrogate, Smilin' Stev. Some time ago he served the Gilded Duke as a smith. When that worthy fell afoul of, and was vanquished by, Baron Klaus Wulfenbach, his retainers were dispersed in the Baron's customary style, and instead of the usual back pay, he accepted Smilin' Stev as payment in kind. How he then wended his way to the Circus is not totally clear. Somewhere along the line he met his mate, Trish Belloptrix, and produced Balthazar. According to Balthazar, Guntar says Trish likes her men "big and slow and stupid," from which you can infer what you will.
He commonly plays Punch in the Heterodyne Show plays. Though after finding out from Da Boyz that the real Punch was much more intelligent than he is commonly portrayed, he is shown trying to give the role more dignity.