外子 an archaic term, parallel to calling one's wife 内子. It was very common in Song dynasty（between 960 and 1279). Regarding its origins, the third volume of 《恒言录》 written by 钱大昕, a famous scholar in Qing dynasty（1636-1912), gives the following origin for 外子: "in Liang dynasty, a country during Southern and Northern Dynasties of China(420 - 589), the poet XuFei wrote a poem called “赠内诗" and his wife wrote a poem called "答外诗," and that's the origin of 外子 and 内子. By the way, 内子 and 外子 can only be used by a couple to refer to each other, meaning that you can call your husband 外子 or your wife 内子, but you never can call another women's husband 外子 or another man's wife 内子. Lastly, what I want to say is that now we never say 外子 and 内子 in Chinese-speaking countries, including China, Taiwan, Hong Kong, and Singapore.