If it is a very close friend, it is similar to your custom.
If it is not a very close relationship, then normally each person will pay individually. If someone wants to do something special for the other person, they will offer to pay. But sometimes, the other person will not allow it because they don't want to impose on someone else.
Yesterday I had breakfast at a restaurant, and I offered to pay for the meal, and she accepted. I enjoy paying for friend's meals, especially if I know that they may need the help to pay for things. I used to not be able to eat at restaurants because it was too expensive, so now that we have a little extra money in our budget, I like to help others pay.
I also allow others to pay for me because I don't want to withhold a good feeling from them. In America, it feels good to offer to pay for someone's meal, so why would I want them not to feel good?
Usually, if someone offers, I will say, "Are you sure?" and if they say, "Yes, I would really like to pay," then I will say, "Thank you. That's very nice of you." Or something similar to this.