I understood that nationality was based upon the country in which you were born. The child of a Portuguese couple living and working in the Channel Isles and born there is therefore British. Similarly, like the OP, the child is a US citizen But
I further understood that the child of a Service family born abroad has the nationality of the father's normal domicile. On that basis my mother born in India was Irish but then had difficulty getting a British passport as Ireland was now outwith the UK. Further my granddaughter born in Cyprus is also British.
In the US case it may depend on the Status of Forces agreement, for instance what of children born in UK to US personnel?