Azure allows to have only two external IPs per VMs network adapter: Virtual IP (VIP) and instance-level public IP address (PIP). Please see more details regarding Azure IPs: http://blogs.msdn.com/b/cloud_solution_architect/archive/2014/11/08/vips-dips-and-pips-in-microsoft-azure.aspx

Some Azure Tiers allow to have multiple NICs per VM. More details: https://azure.microsoft.com/en-us/blog/multiple-vm-nics-and-network-virtual-appliances-in-azure/. But you can not attach multiple IPs to these NICs.

Thus in most cases you need to use NAT to give your containers access to external networks. Please follow instructions in this article: https://openvz.org/Using_NAT_for_container_with_private_IPs