It sounds idiomatic to me. Here are some other examples of "normal woman" being used outside of health or mental health contexts.
Normal can mean "not a radical feminist". Finding a ‘Normal’ Woman: Selection Processes for Board Membership:
"They told me they wanted a woman on the board who was married, who had children, who had her master’s degree, who had experience in the labor market, but was still a ‘normal’ woman and not a radical feminist or a battle-axe. .... also someone who does not get sidetracked by details."
Normal can mean not a part of the "rigidly policed ideal of beauty – young, skinny, white, impossibly beautiful". Put a normal woman in a bikini. That’s how to bust the beauty myth:
Put a normal woman in a bikini and it’s obvious how little of the magic is down to the clothes, how hard magazines have to work just to make them look interesting.
Normal can mean someone who's acting like she's not a superhero. Sarah Nicole Prickett on the Myth of the Wonder Woman:
“I’m almost jealous of myself as Wonder Woman,” she thinks in one early issue, from the Marston/Peter years. “Nothing I do as a normal woman, Diana Prince, ever impresses anybody.” Like a normal woman, she can, as a matter of fact, do several impressive things her boss cannot. She is always loaning him confidence, free of interest. She takes excellent dictation and types like hell, and Steve says she is “quite the little psychologist.”
The first one is still an example of "normal" being contrasted with something negative, but the other two are examples where "normal" means "not extraordinary", the same as it does in your context.
I don't think "common" would work here (but "ordinary" would), since "common" can mean "without rank", changing the intended meaning.