I recently went through analysis on Docker for this type of setup. I know there are some who view Docker as a sort of MicroVM, but my take is the Docker philosophy leans more toward single process per container. This tracks well with the Single Responsibility principle in programming. The more a Docker container does, the less reusable and more difficult to manage. I posted all my thoughts here:
http://software.danielwatrous.com/a-review-of-docker/
I then went on to build a LEMP stack using Docker. I didn’t find a lot of value in splitting the PHP and Nginx processes into separate Docker containers, but the Web and Database functions are in separate containers. I also show how to manage linking and volume sharing to avoid running SSH daemons in your containers. You can follow what I did here as a point of reference.
http://software.danielwatrous.com/use-docker-to-build-a-lemp-stack-buildfile/
To your point about increased complexity for the single function per container, you are correct. It will look and feel just like you had distinct, distributed tiers. Very large applications have done this for years and it does increase complexity when it comes to communication, security and management. Of course it brings a number of benefits as well.