Of course we can have moral without religion. The Bible proves that we can.
Okay, let me explain!
Every group, organization, social structure has an ethical principle that there members are supposed to follow. It may be the ethics (Hippocratic oath) our physicians follow or it may be how a society makes it's formal laws.
A doctor is bound by his ethics, but will still follow his personal moral believes when it comes to a question about saving life thru blood transfusion (LDS). And you and I will follow the social accepted norm/moral when driving our car just over the speed limit. Not enough for a ticket but enough to break the law. If you still get a ticket for that you will most likely gain sympathy instead of a lecture, about how important it is to follow the letter of the law.
We have ethic norms in our society that differs from place to place depending on where in the world we are. In Sweden we do not have capital punishment and we do not allow corporal punishment against women/children in schools homes or anyplace, banned 1966.
Now in a society were capital punishment is a part of the overall ethical system a greater acceptance towards corporal punishment follows (not necessary always). "Nobody is going to tell me what I can or can't do in my own home!"
And if you then ad religion were you have a book that support your societies ethics then it's easy to say - It's okay to beat your wife/child as long as you do not break bones, makes marks on the face or leaves marks on the body.
(Disgusting, if I can't see it. It never happened!)
What I just stated is, that in the Bible you have the ethical principles for the believers but it's actual moral is based on the followers/believers upbringing and surroundings.
All believers demonstrate a personal non-religious moral when they "Cherry pick" the Bible by saying that it's "just a metaphor" or "Ohh! That's the Ooold Testament" when we talk about stoning or killing or whatever that we (atheist) think is morally wrong.
The Bible with all the "Thou shall not..." or "If a man..." or If a woman..." is so conflicting that you have only one way out of it's bad ethical norms and that is by following your own moral when it actually comes to "do-the-right-thing".
We all are moral regardless of the bible. Moral or immoral is just the answer to if we are following the groups code of conduct (ethic) or not.
You talk about Ethic (separate right from wrong, and agree that it's the right thing is to stone/flog your daughter) and you do the morally correct thing by not stone/flog your daughter.
The moral behavior is not a textual thing that you find in the Bible. It's what you find in peoples behavior regardless of ethic textual teaching.