What I went with was having both a web server (Apache/Nginx) and PHP-FPM in the same container image, held together by Supervisor: http://supervisord.org/

In my case, the Dockerfile looks a bit like the following:

  # Whatever base web server image you want, Debian/Ubuntu based here
  FROM .../nginx
  # Bloated packages for installing dependencies and other stuff
  RUN apt-get update \
      && apt-get -yq --no-upgrade install \
          software-properties-common \
          supervisor \
      && apt-get clean \
      && rm -rf /var/lib/apt/lists /var/cache/apt/*
  # Add repository for PHP 8
  RUN export LC_ALL="C.UTF-8" && add-apt-repository ppa:ondrej/php
  # Then we install PHP and the Nginx integration package (we use PHP-FPM)
  RUN apt-get update \
      && apt-get -yq --no-upgrade install \
          php8.2 php8.2-common php8.2-cli php8.2-dev php8.2-opcache ... php8.2-pdo-mysql php8.2-mysql php8.2-xml php8.2-imagick php8.2-fpm \
      && apt-get clean \
      && rm -rf /var/lib/apt/lists /var/cache/apt/*
  # We will also need Composer for managing dependencies
  RUN curl -sS https://getcomposer.org/installer -o /tmp/composer-setup.php \
      && php /tmp/composer-setup.php --install-dir=/usr/local/bin --filename=Composer
  # Create directories
  RUN mkdir -p /run/php \
      # Clear regular web server index directories
      && rm -rf /var/www/html && mkdir -p /var/www/html
  # Copy over config
  COPY ./php_nginx/etc/nginx/nginx.conf /etc/nginx/nginx.conf
  COPY ./php_nginx/var/www/html /var/www/html
  # Copy PHP config
  COPY ./php_nginx/etc/supervisord.conf /etc/supervisord.conf
  COPY ./php_nginx/etc/php/8.2/fpm/php.ini /etc/php/8.2/fpm/php.ini
  COPY ./php_nginx/etc/php/8.2/fpm/php-fpm.conf /etc/php/8.2/fpm/php-fpm.conf
  COPY ./php_nginx/etc/php/8.2/fpm/pool.d/www.conf /etc/php/8.2/fpm/pool.d/www.conf
  # Default run script
  COPY ./php_nginx/docker-entrypoint.sh /docker-entrypoint.sh
  RUN chmod +x /docker-entrypoint.sh
  CMD "/docker-entrypoint.sh"

Here's the entrypoint:

  #!/bin/sh
  echo "Software versions..."
  nginx -V && supervisord --version

  echo "Running Supervisor..."
  supervisord --configuration=/etc/supervisord.conf

And here's the Supervisor configuration:

  [supervisord]
  nodaemon=true
  
  [program:php-fpm]
    command=/usr/sbin/php-fpm8.2 -c /etc/php/8.2/fpm/php-fpm.conf --nodaemonize
    stdout_logfile=/dev/stdout
    stdout_logfile_maxbytes=0
    stderr_logfile=/dev/stderr
    stderr_logfile_maxbytes=0
  
  [program:nginx]
    command=/usr/sbin/nginx
    stdout_logfile=/dev/stdout
    stdout_logfile_maxbytes=0
    stderr_logfile=/dev/stderr
    stderr_logfile_maxbytes=0

Of course, it isn't necessarily the most idiomatic way to work with containers, but if you have health checks then it should still be fine. With a base image a little like this, you should then be able to build your own images with the code included, or use a bind mount.

Notes: you can probably get images that work a bit like this pre-made, this is just how I do things, in case you're curious about what that might look like. Apache also has mod_php which would be even simpler, though generally will perform worse than PHP-FPM.