From my experience and reading completely conflicting sources while having no formal education in the matter there seems to be two schools of thought on the matter
One way of looking at it is this way:
Here God's laws are on top and man's are on the bottom it's ordered by jurisdiction. Here the eternal law that is on top is the Unchangeable Nature of God, His Might, Glory, Power and Awesomeness.
Next is the Divine Law, which is what he tells us about Himself.
The line is there to divide God's laws from man's laws which is as big a chasm as there is
Then is the Natural Law, which is the law written on the hearts of man and accessible to man through reason alone. (I'm not sure if this actually includes the natural sciences or not, but if it does, then more power to it)
then is the Human Laws, like requirements that people in a neighborhood have a certain color curtains as well as evil and arbitrary laws like Jim Crow laws in the American south and ones leading to the Nazi Holocaust.
the other way of looking at is is in a hierarchical manner. You don't get any order of magnitude, but you can see which are made up and which are innate.
Here is the division between Natural Law and Positive Law. On one side there is what is classically described as the Natural Moral Law and that's everything that seems innate to nature. When Aristotle looked at a rock and said, "what does it do?" he was describing the Natural (Natural) Law when Plato considered the God of the universe and said, "what does He do?" he was describing the Natural (Eternal) Law.
On the other side, as with the above description are the seemingly arbitrary laws.
The divine side of positive law is the commands of God. This is the stuff atheists hate. It is also the stuff by which man must supplement his bread if he wants to live. The covenants God makes with man are Positive (divine) law.
Then positive (human) law is the same as described above.
Speaking in the basest way possible about things I hold sacred, religion only puts things in "divine". Eternal and natural law are accessible to reason and therefore in the realm of philosophy, not religion. Catholics, at least, are called to respect the laws of the other religions insofar as they reflect God's truth. We don't say our religion has the 'fullness of truth' to be all high and mighty, but because we know that other religions have a share in that truth.
Those who do not believe in God, or only believe in Him through reason, might argue that Divine Law is arbitrary, and one would have a hard time arguing with that because it is true. They might argue that it is man made, and one would have a hard time arguing with that because it comes to us through men. However, they can't win an argument on the premise that divine law (i.e. biblical revelation) conflicts with eternal law and this is (one reason) why Christianity is true.
Natural law, however, is changeable, as nature is changeable. For instance, if humanity was struck with a fit of incurable hermaphordism, then I'd imagine homosexual marriage would be acceptable under the natural moral law. The difference between Natural law and Eternal law is that Natural law is applied to God's creation and created things are always in flux. This does not mean, however, that it is up to man to decide when they've changed or whether or not they really exist; that is why the Natural Moral Law is incompatible with moral relativism.
However, and to your question, there is a Moral aspect of Divine Law. Which is how the Decalogue goes from being written on your heart to being written on tablets.
...all the precepts of the Decalogue are also precepts of the natural law, which can be gathered by reason from nature herself, and in fact they were known long before Moses wrote them down at the express command of God. This is the teaching of St. Paul —
"For when the Gentiles, who have not the law, do by nature those things that are of the law; these having not the law [of Moses], are a law to themselves: who shew the work of the law written in their hearts, their conscience bearing witness to them"
(Romans 2:14, 15).
Although the substance of the Decalogue is thus both of natural and Divine law, yet its express promulgation by Moses at the command of God was not without its advantages. The great moral code, the basis of all true civilization, in this manner became the clear, certain, and publicly recognized standard of moral conduct for the Jewish people, and through them for Christendom.
So it came to pass that the natural moral law was codified as the divine positive law. One might even say, to it's detriment, as the Ten Commandments are now prohibited and contentious religious symbols. But, I wouldn't say it is to the detriment of the natural law. In a world where people are free even to deny the foundational principles of their soul, our God has given us two reasons to believe and follow his commandments.