Actually, It looks like Alex is not a stay at home dad, a few pages back it was said that he works from home.. not sure what he does, but he does have a job.
I just had a thought.. What if John is not the Biological father? What if this woman is a close friend of his, and she selected John to take custody of her child in the event of her death, and because of what he just said here, hes more than willing to raise her child as his own because of what she did for him?!
To answer your actual question, No, I don’t think it has ever been stated before, in the comic, who Aj’s biological father was (It is not important to the over all story at that point).
As for his biological mother, where was a post on Mother’s day Last year with a “Mysterious” framed picture of a woman on it, that many are assuming is a picture of AJ’s biological mother (http://www.gocomics.com/aj-and-magnus/2017/05/14)
Gods dammit.. I really hoped the feeling of foreboding I got after Joe met Alex was wrong.. guess not. :(