I'm my opinion it's not a question if what is usually acceptable.
In this case it's simply that the husband is not comfortable with his wife doing this.
In a relationship there are compromises to some extent. I'm sure if the wife feels it's important for her to join, she'll try to work that out with her husband.
Sorry, but tubes are significantly better for off-road performance. What do you off-road?
Edit: I can't really say why I wrote this comment like this. Very aggressive. Sorry again.