am I being fair to want supervised access? How long will they be supervised?

-he is verbally abusive to child and myself- the mother. screaming at child calling names etc. -uses heavy drugs and marijuana in front of child.. drives high.. etc is inconsistent, doesn't show up etc mentally unstable, takes medications(atavan) and he is still very aggressive, depressed, etc. bi-polar type behaviour.. calm to yelling alcohol abuse-child has been exposed sexual behavior in front of child child got into his medication after he was told repeatedly to keep all medications up shows no initiative. sees child for a time period of 20-60 minutes once a month. once a week during summer months. he lives four hours away during fall-winter months. unwilling to change, cant communicate or talk just gets aggressive and defensive. he has not taken child unsupervised in over a year. will judge find only supervised access reasonable? what can he do to try to get unsupervised access and in what sort of time frame could he get unsupervised access? child is 3