It's a fact of life that the role of 'military spouse' is usually very much an adjunct to the 'head of the family'. It's visibly out of step with how many other people live their lives now, which has been recognised as an issue, but that's not to say it's "wrong". It's difficult however to find ways that partners of military personnel can themselves have a career when the demands of the military half of the couple are so unpredictable, involve moving around every couple of years, off for six months at a time on one of Her Majesty's Holidays (tm)...
They just happen to mostly be women in this case, which wasn't (initially I think) set up at all to be a TV series with a spin-off single, it was a fly on the wall (ish) reality/documentary. It was a lovely, sweet three part series which grew legs and arms.
I can't see a big feminist issue in this, except to say that I've (formerly) been a woman in the army for a short while, and I still know a lot of women in the forces. The character types they tend to have as partners are not often the SAHP / significantly lesser earner / content with being defined as "husband of...". I also know lots of men in the forces who have wives/partners with "proper" careers themselves, who therefore don't define themselves as 'wife of', either.
I expect that the proportion of military families who rely on a single/main income is probably higher than in society at large, and it would follow that as there are more men in the military those "spouses of..." are largely going to be female, but it is by no means the only way that military families work. I think the group who are entitled to be most narked with the (well-meaning, but fairly one-dimensional) characterisation of the programme/song publicity are military wives with jobs who don't live on a camp, because I bet a few of them are getting asked 'are you going to join if they set one up where you are?', and having to explain it's not compulsory to live in tied housing and take a full part in the military family thing.