Hypothyroidism Support Group
Hypothyroidism is the disease state caused by insufficient production of thyrohormone by the thyroid gland. There are several distinct causes for chronic hypothyroidism, the most common being Hashimoto's thyroiditis and hypothyroidism following radioiodine therapy for hyperthyroidism. Advanced hypothyroidism may cause severe complications, the most serious one of which is...

The whole reason we do well when taking thyroid replacement is because our body needs a steady supply of thyroid hormone to meet the needs of every single cell in the body.
I really don't see how anything can improve hormone levels in the body if the gland that's supposed to produce the hormone is unable to do so because of disease.
This link discusses the issue where HGH is recommended and what the risks are.
http://www.webmd.com/fitness-exercise/human-growth-hormone-hgh
Here's just a few:
Possible side effects of HGH use include:
nerve, muscle, or joint pain
swelling due to fluid in the body's tissues (edema)
carpal tunnel syndrome
numbness and tingling of the skin
high cholesterol levels
HGH can also increase the risk of diabetes and contribute to the growth of cancerous tumors.
Perhaps your hubby has something different - and HGH does affect men differently than women (testosterone and all that).
And NO - Can't find anything other than thyroid hormones that helps my levels (and believe me I've tried).
Maybe if you put it in those terms, he'll understand a bit better?
Basically, you have to put yourself first....ahead of the temporary satisfaction of others. For instance, going off your thyroid meds for this HGH stuff might make him feel better in the short term, but I don't think he'd be happy with a wife who's in pain all the time and has NO interest in sex. Because hypothyroidism causes that. I don't think he'd be happy with a wife who dies of heart disease either. So, love yourself first. Treat yourself first. Leave others to their own devices and put things in terms they can understand. Like, "No meds. No sex." ;)
Treating a chronic disease is working the long term game....not the short term. Keep your chin up, and do what's best for YOU>