You mean something like this?

Remember that Text widget has always padding on top and bottom that is build into the font — you would need to play with the padding of the image to be the same.

The solution with the CustomMultiChildLayout should work:

CustomMultiChildLayout(
  delegate: new _Layout(),
  children: <Widget>[
    new LayoutId(
      id: Colors.red,
      child: new Container(
        color: Colors.yellowAccent,
        child: new Text(
          'Hi',
          style: new TextStyle(fontSize: 60.0),
        ),
      ),
    ),
    new LayoutId(
      id: Colors.blue,
      child: new Image.network(
        'https://flutter.io/images/flutter-mark-square-100.png',
        fit: BoxFit.fill,
      ),
    ),
  ],
),