This is one people keep asking me which Microsoft hasn’t published officially. Currently Microsoft Azure allows you to have a public and private load balancer in front of the same availability set.
You can also link both load balancer to the same machines in the availability set. This will enable your servers to have a load balanced private and public IP, which comes in real handy.
You can also link the public to some of the machines and the private to other machines in the availability set.