Your home state of Illinois follows a Tort system meaning someone must be found to be at fault for causing the accident, and that person and their insurance company is responsible for all the damages.
Illinois state law requires minimum Bodily Injury Liability coverage of $20,000 per injured person up to a total of $40,000 per accident, and Property Damage Liability coverage with a minimum limit of $15,000. This basic coverage is often referred to as 20/40/15 coverage. Illinois state law requires a minimum UnInsured/UnderInsured Motorist coverage of $20,000 per person, $40,000 per accident for any bodily injury caused by the uninsured driver.
While the state of Kentucky follows a No-Fault system meaning a person's insurance company will make payments for their injury claims regardless of fault, up to a specified limit.
Kentucky state law requires minimum Bodily Injury Liability coverage of $25,000 per injured person up to a total of $50,000 per accident, and Property Damage Liability coverage with a minimum limit of $10,000. This basic coverage is often referred to as 25/50/10 coverage.
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So, no unfortunately Kentucky's no-fault insurance will not help you or your husband in anyway. Basically no-fault insurance normally deals with injuries of drivers. As the KY Department of Insurance explains the term no-fault insurance is commonly misunderstood term because it has nothing to do with who was responsible for the accident.
Here in KY it applies to personal injury protection (PIP) which in this state pays the policyholder up to $10,000 for medical expenses, lost wages and other incurred expenses due to injuries sustained in an auto accident, regardless of fault.
Thus since you have liability only and were at fault, your property damage liability should pay for the damages the other vehicle sustained. For your vehicle to be covered for repairs you would need collision coverage on it. | 
