It's my understanding that you would do this the exact same way like with any other VM to join a domain:

https://learn.microsoft.com/en-us/azure/active-directory-domain-services/join-windows-vm

The distributed marketplace template creates it's own networking and doesn't use an existing vnet, and you create user accounts for the VMs (it doesn't use domain accounts).

To RDP into the machines created by the marketplace distributed deployment you will have to use a Bastion or just use a VM as jumpbox which is in the same VNet as the VMSS. Also the domain server needs to be reachable within this VNet. This could possibly be achieved with VNet peering.

As a warning, the default marketplace deployment is not production ready and it is highly recommended to add security rules to the vnet limiting traffic to the minimum possible. We recommend that you download and modify the marketplace template as needed to fit into your cloud environment, or create your own using ours as an example.

Thanks Jen for the answer.

This is our third install/upgrade in Azure so we wanted to see what the newest options are.

We think making the template would take longer than the traditional install.

Factors include that we use a third party to manage our cloud environment who would have to make the template. We also use an IIS URL rewrite.

For now we continue with the traditional install.

Annette