I’m using Tempera template. With this template you can set Featured Images in the article of both Pages and Posts.
Perhaps you actually are looking for a “Widget” on your homepage to get what you want. Check if your template offers a widget you can use for this. With Tempera you can use a “Cryout Column” widget on your homepage with text and images, via Appearance > Widget > Presentation Page Column > drag&add Cryout Column and fill in text and image.
Hope this helps.
