Yea that is one of the reasons the theme uses the_excerpt instead of the_content for that area.
You can instead change back to the_excerpt and then add this for a read more link, where you want it to show up in content.php:
<a href="<?php the_permalink(); ?>">Read more</a>
Alternatively, make sure to always insert images in the post after the more tag.
Or you could force-hide images with css for the excerpt area:
.entry.excerpt img { display: none; }