This one is actually pretty easy.
Presuming that the coroner can determine that the cause of death was the gunshot rather than the fall, and presuming that this event occurred in Illinois, I'd say that the husband should be guilty of involuntary manslaughter. The relevant language in the criminal code
(720 ILCS 5/9-3) (from Ch. 38, par. 9-3)
Sec. 9-3. Involuntary Manslaughter and Reckless Homicide.
(a) A person who unintentionally kills an individual without lawful justification commits involuntary manslaughter if his acts whether lawful or unlawful which cause the death are such as are likely to cause death or great bodily harm to some individual, and he performs them recklessly
The husband's act of shooting a gun at his wife was such that it was likely to cause death or great bodily harm. Granted, the husband would argue that he was aiming at his wife rather than the falling suicide, but the statute only says that his actions must be likely to cause death or great bodily harm to some
individual, not necessarily the person he was attempting to kill. And it will avail him little were he to claim that he thought the gun was unloaded. It was his misfortune that the gun was
loaded, and it was his duty to make sure it wasn't. Indeed, aiming a gun at someone and pulling the trigger on the assumption
that it is unloaded is the height of recklessness, which completes the requirements for the crime.
I'd add that the husband would also be guilty of aggravated assault, but that doesn't seem to have been an issue for the writer of the hypothetical.