Totally agree with what everyone else has said, this is classic resource guarding - super common, super fixable, and there are tons of resources on the Internet that will help you guys overcome this.
I would even go one step further and ban him from the couch entirely, at least for now. Get a dog bed or mat and position it in the room where your couch is and teach him the ‘Place’ Command. If he already knows ‘down’ and ‘stay’, those come in handy too. He shouldn’t be on the couch at all while you or your wife or both are on it. Dogs that don’t have couch manners = don’t get to be on the couch (keep this consistent and don’t cave, no exceptions). It also gets him accustomed to seeing the two of you together without him - maybe even over-exaggerate a cuddle or kiss for his benefit. This isn’t a punishment so much as just teaching him where he fits in the dynamic between the three of you. He’s been getting the wrong message up until now (through no fault of your own or your wife’s!! No one can predict that a dog will respond this way to their primary caretaker), that your wife is a threat to his possession of you, rather than a high ranking member of the family with partner and couch privileges too.
(If he sleeps in your bed, same rules apply)
Eventually you might be able to transition him back onto the couch - I would wait until you don’t see any resource guarding behavior for at least several weeks. This is in conjunction with everything else people have said - your wife should be the one to feed him and walk him. You, as hard as it’s going to be, should not offer him any (or at least very, very minimal) physical affection during this time. You’re going to want to cave and that’s understandable. it’s really hard not to give your dog long pets and cuddles, but resource guarding only gets worse over time (growling becomes lunging, lunging becomes biting). Better to nip it in the bud now quickly and decisively.
Edit: oh, and number one thing not to do is ‘redirect’ him with treats. I.e., ‘Your wife comes over, he growls, you/your wife make him get off the couch, then give him a treat’. ‘Or your wife comes over, he growls and you/your wife give him treats’. That’s not redirecting anything, it’s rewarding his growling with food and he will very quickly make that connection and it will very quickly get worse. Food should not even be in the equation during this ‘correction’ period (except in the training and reinforcement of the ‘Place’ command, or ‘down’ and ‘stay’ commands designed to preemptively make him give you and your wife space before he even has an opportunity to resource guard). Basically, At no point should any resource guarding behavior be followed by treats.
