I wouldn't be at all happy.
She is emotionally vulnerable, perhaps feeling shitty about herself - depending on why her relationship ended, and therefore may love a man's attention.
What isn't healthy is her using your DH as an emotional prop - almost as a substitute partner.
There is no reason for him to be picking her up from stations late at night - there are taxis for that, or she must have other friends/family to do that for her.
I can understand that he might not like the idea of her being alone late at night, waiting for a taxi, but really, she is just a friend, it's not his responsibility to look out for her welfare to such an extent. He will revel in this 'being needed', and that is where the danger lies.
Popping round to hers on the way home, alone - definitely not cool, if he didn't use to do it when she was in a relationship - then there is no legitimate reason to be doing so now.
When I moved closer to my parents (before I met DH), a married friend of theirs, started coming round - he started coming round after I was raped by my ex.
It started to become regular, and he was nice, I trusted him (known him for years), and enjoyed his company.
I used to ask if his wife minded, but he said she didn't (I was friendly with her too, and he used to phone me & she was there when he did so).
One day, he decided he was 'in love' with me. He even came to see my dad, to tell him that he planned to leave his wife for me.
At this point I broke off all contact with him. I'd never encouraged him at all, but if something happened (like my windows being smashed one night), I would phone him, and he'd come. I'd never encouraged romantic interest - but I was a single female, and he liked to be my protector, check up on me, feel needed by me.
Luckily his wife never found out (she still speaks if I see her), and he re-invested in his marriage.
The upshot - I would never let any partner of mine do too much for another woman - even a mutual friend.
It sounds like he may be developing a crush on her, but irregardless, it is dangerous for him to take any responsibility for her - the lifts home, popping round alone etc, have got to stop