Personally I would tell him not to take the Ambien. It sounds to me that your doctor is not addressing the issue. I suggest changing doctors. Go with the 'I'd like a 2nd opinion' tack.
What level of dose is your husband on at the moment? How long ago did he have his thyroid out? It can take up to 6 weeks for any dosage change to take effect.
Is he taking his medication in the morning and then waiting at least an hour before food? It is very important he not eat (can have drinks) till at least an hour after taking the medication. Reason being it is absorbed by the food and he may as well not take it!
It can be very tricky to get the levels correct.
I had my thyroid removed and had a heck of a time at first.
Please post his latest thyroid levels - as Deb said - TSH, FT3, FT4, along with the reference ranges, as these are lab specific and must come from his own report.
I would agree that he probably needs an increase in med, but you can't know unless he's tested.
Get his thyroid levels checked...FT3, FT4 and TSH.
Also get his Calcium, B12 and D3 checked.
Sounds like Hubby may need an increase in medications but needs labs done first.
Slow is good with thryoid meds as he could go drug induced hyper if done too fast.
And with all thyroid issues...it IS a slow long road but he will get there :o)