We have spent the last month in Bhutan, Nepal and lastly in Tibet at varying altitudes from 2,400m - 5,500m (7,800ft - 18,000ft). Only for the last stage of our travels in Tibet (Several high-altitude temples & Everest Base Camp) did we take any medication for altitude sickness, solely as a preventative instead of a cure.
The most popular brand is "Diamox" (http://en.wikipedia.org/wiki/Acetazolamide). There is also several alternative medicines including a herbal substitute that I have heard of which may assist as well. But as with anything, please consult your chemist or doctor if you are taking any additional medications to see if they will react with each other.
As a relatively unfit 60 & 63 year old couple we did not have much problem with the altitude at all, even at Everest Base Camp. However you must increase your daily water intake substantially as the body requires much more water the higher you go. We drove in through the Nepal/Tibet border which was the 'harder' way to go regarding the altitude and we are fine. We seem to wake up each morning with a blocked/slightly blood nose, but that clears after you get up and blow it.
The biggest issues we had was actually with the Diamox tablets themselves. It gave me incredible nausea every time I took a tablet which lasted for hours, and our 23 year old son who came with us had tingling fingers whenever on the medication. We actually ceased taking it halfway through Tibet and all side effects have stopped and we actually feel quite good.
The only foreseeable difficulties I see may arise if you or your husband have asthma or are smokers, as breathing is slightly more demanding in Tibet. The air is clean, even in the capital city, Lhasa, where I write this now, I can clearly see mountains and little pollution.
Another web-link that may assist you is en.wikipedia.org/wiki/Altitude_sickness
On a side note, everybody will react differently with altitude, and I strongly recommend bringing some medication to assist with both Constipation and Diarrhea - only from experience!