Assuming you didn't provoke the dogs, the owner is absolutely liable to you for damages. You are entitled to recover your medical expenses, any wage loss, and any other out-of-pocket expenses, plus damages for pain and suffering and any fear, anxiety, disability or scarring caused by the bites. All of your damages should be paid by the dog owner's homeowner's insurance.
If you need assistance in prosecuting your claim against the dog owner, call my office for an appointment. This is one of my areas of specialty.
It depends on the amount of damages you sustained, i.e. medical costs, time missed from work, future medical care. You'd also be entitled to some damages for pain and suffering, also known as general damages. Liability seems to be pretty clear so you should contact an personal injury attorney to explore your options.