Invisalign Instead of Orthognathic Surgery?

It sounds like you have a skeletal problem where your upper jaw is too far behind your lower jaw (or the lower is too far in front of the upper).  Invisalign does not address jaw alignment problems at all, and so would not be a reasonable alternative.   Sometimes, if the discrepancy is not too great, a mild underbite can be corrected by extacting one front or two back lower teeth and using conventional appliances to pull the lower front teeth back into a normal bite.  However, this "camoflage" treatment does not actually correct the skeletal problem and will not appreciable affect the facial profile.  An experienced orthodontist can evaluate your case and discuss all the options with you.

Your orthodontist should of treated both arches when you were an adolescent. As an adult you should seek a new evaluation from an orthodontist, have them take a panoramic and cephalometric radiograph to assess what can be done to help improve your bite. Braces and the use of elastics/rubber bands can help your bite slightly, but if you have a skeletal abnormality it can only be fixed by orthognathic surgery. Your teeth sit on the bone, you can't move the bone, you can only tip the teeth.