I am trying to deploy 2 containers on 2 different tasks (1 container per task), one is my frontend and the other is my backend server. I am trying to figure out how to configure the communication between them.
I saw that a load balancer in a service is a good option. However, should I configure load balancer for my front end server and another one for my backend? Meaning each time I have public-facing services and private services I need 2 load balancers?
I would like to only expose my front-end to the public internet and my backend will remain private (although I make API requests to the outside world - probably need to configure outbound route too?).
I would highly appreciate any information.
No you don't need a private LB for that. It is an option you can use but ECS has since introduced the concept of Service Discovery for back-end services. The idea is that your front end is exposed to your users via a standard LB (e.g. ALB) but services that are being called by the front end and that run behind the scene can be addressed using this service discovery mechanism (based on Route53/CloudMap).
You can see an example of this concept here. This CFN template gives you the details re how you can build this layout.