Q.  Psychiatrists say that someone is mentally ill. But, is there such a thing as mental illness? And, if there is such a thing as mental illness does that mean that the person cannot help being so sinful? Is mental illness an excuse for sinful behaviors? Or is the sinful behaviors the cause of the mental illness? For I have read that Jesus did not heal one mentally ill person. 

A.   Some "mental illness" is caused by physical deficiencies, i.e., a chemical imbalance in the brain, and can be treated by medicine - or healed by God. 
Some behaviors that might be interpreted as "mental" go much deeper, and are really caused by spiritual depression. A person might be struggling with rejection, for example, and act out in anti-social ways that seem odd - but are neither physiological nor spiritual in nature.
Some mental problems are caused by demons, and no amount of medicine or psychological therapy or psychiatric treatments can help - only spiritual deliverance can set the person free. 
The gospels tell of a man who hung out, naked, in the tombs, cutting his flesh. Jesus' response was to cast a demon out of him - after which the man was then found "in his right mind," it says. 
No one can evaluate your husband's problem over the Internet. First of all, it's being filtered through your understanding - and his real situation might not be the same as you perceive it to be. I would advise you to seek professional help - pastoral as well as medical - for both of you, as you are "one," and his problems are your problems.

As for what the Scriptures say about Deliverance from evil spirits (which may or may not apply in this case), following is a bible study outline on the topic: http://www.dianedew.com/deliver.htm