Please try not to worry about it
though I know that's easier said than done at this unnerving stage of our lives. The interaction is said to occur only with oral oestrogen, which as your husband has read
can increase our need for thyroxine. The mechanism is that the oestrogen increases something called Thyroid Binding Globulin (usually abbreviated to TBG) which yes, can mean that there is effectively less thyroid hormone available for use in the body. Many hypothyroid women use HRT & find with transdermal regimens that their thyroid levels remain stable & research studies bear this out. But just a few of us on here on transdermal HRT have found we also need to tweak our thyroid replacement slightly when starting/increasing/reducing our HRT & my (very senior) Endocrinologist has confirmed it does happen.
It's usually recommended to have a TFT 6 weeks or so after starting HRT & again at 3 months, but your GP may not think this necessary on transdermal. Personally, I would ask for it to put your mind at rest. It should be easy to adjust your thyroid dose with your doctor's guidance if need be, but chances are you won't need to.
Wx