Euthyroid : This means normal thyroid hormone output is found in blood tests. The patient (hopefully) feels well.
Hyperthyroid : This means "overactive". The thyroid is producing too much thyroid hormone (or too much is being taken as a medicine/drug) for long-term good health, and people will feel ill.
Hypothyroid : This means "underactive". The thyroid doesn't produce enough thyroid hormone for good health and/or the medicine or drugs being given are inadequate. The patient will feel ill in this condition too.
The ranges used for people after thyroid surgery should be the same as for healthy people. If your body needs a certain amount of T4 and T3 before the surgery, then it still needs the same amount after surgery. If you can find out what levels your husband had before surgery, then the closer you can get to those with medication after surgery the more likely he is to feel well.
Nutritional deficiencies are very common, as has been mentioned already. Since your husband has had surgery there is a very important issue that can arise with vitamin B12.
If the anaesthetic used contained nitrous oxide (many of them do, it is very commonly used in surgery), it oxidises the B12 in the body and it becomes useless to the body. So the patient starts developing serious deficiency problems, even if the B12 level appears normal in blood tests. So, your husband needs to replace the damaged B12 as soon as possible because B12 deficiency is very serious.
(Where there are references to cobalamin, this is another name used for vitamin B12.)
Do some searches for "anesthetic B12 nitrous oxide" or "anesthesia B12 nitrous oxide".
It would be a good idea to give your husband vitamin B12 supplements in quite high doses. The best one for quick absorption is methylcobalamin. If he takes more than he needs this is not a problem because the body just excretes any excess in urine. It would be good to take 1000mcg - 5000mcg per day - start with the lower dose, some people don't tolerate higher doses. Buy it as a tablet which can be stuck in the mouth somewhere it doesn't feel annoying, let it dissolve very slowly, don't suck, chew or swallow it whole - this helps to maximise the absorption. I buy one from a company called Jarrow Formulas, Solgar is also popular. I don't know what options you have available to you in your country.
Please do your own research and double-check everything I've said. I'm not a doctor!