You are probably liable if you own the dog and the person bitten was in a place they had a right to be and did not provoke the dog. Most states have an Animal Control Act that imposes strict liability on the dog owner. Your insurance should cover it. If not check with a lawyer.
You are responsible for your dog. Period. If he got out and bit someone, he was not safely secured. However, if u think this was your fiancée's fault, u should sue her and bring her in as a 3rd party defendant. Not sure how that will help your love life. You may have to bite the bullet and be responsible or add your fiancee As a defendant.
Regarding insurance, check with your agent. These days, Some insurance companies are not covering dog bites or limiting coverage. If yours does not, you need to buy a rider for additional coverage protecting you before your dog bites again. Good luck!
You should have your insurance policy and your case reviewed by personal injury attorney. Although most states impose strict liability on dog owners for attacks on people, there are some exceptions. For example some states require that the plaintiff establish that the animal had a vicious propensity. In other states there is a defense for the dog owner if the plaintiff was initially taunting or striking the dog. I strongly advise you to seek the counsel of a local attorney.
If you take every precaution to make sure your dog is securely contained in your home, then you should not be held to strict liability. Strict liability, meaning you are responsible no matter what. Instead, the claimant will have to prove you were negligent. Under the negligence theory, you can present the defense of fault of a third person.
If the fiancée allowed the dog to escape, the fiancée could be held liable under the negligence theory. If the owner knew of the dog's propensity to bite, kept the dog inside as a result, but failed to inform the fiancee of this, the court might find the owner negligent.