Well, I know that implanting a fertilized egg directly into the womb is certainly a workable approach (expensive, but it bypasses the tubes completely).
You're referring to your tubes, right? (& not a vascetomy in him where he's had his tubes snipped & tied)
Aritifical insemination is usually just mechanically (using a kinda turkey baster but more clinically appropriate) squirting his or a donor's semen into you. If your tubes were tied then your eggs aren't being released usefully (and I don't know about surgical methods to deal with that situation, as I really do not think it would be useful to try to dig into an ovary to retrieve an egg). The question to ask your doctor would be: can your tubes be untied and reconnected so they work again? If not, I think your womb might still be used to implant a fertized egg but the egg would need to come from a donor.