These are individual elements that cannot be individually be targeted. In order to move all thee parts as a unit, we first need to combine them into one element. Pretty cool, huh!

Sources:

• Blog: https://www.peeayecreative.com/how-to-move-the-divi-blog-title-text-and-button-over-the-image/
• Projects (different code): https://www.peeayecreative.com/how-to-move-the-divi-portfolio-title-and-meta-text-over-the-image/

How to

• Add this class to the blog module: pa-blog
• Add this script to a code module on the page or in Divi » integrations » head
• You can now target the new pa-blog-text to give it a background or move it over the image.

// START Combine Divi blog moduletitle, text, meta
<script>
    (function($) {
        $(document).ready(function() {
            $(".pa-blog .et_pb_post").each(function() {
                $(this).find(".entry-title, .post-meta, .post-content ").wrapAll('<div class="pa-blog-text"></div>');
            });

            //Do the same for ajax
            $(document).bind('ready ajaxComplete', function() {
                $(".pa-blog .et_pb_post").each(function() {
                    $(this).find(".entry-title, .post-meta, .post-content ").wrapAll('<div class="pa-blog-text"></div>');
                });
            });

        });
    })(jQuery); 
</script>
// END Combine Divi blog moduletitle, text, metaCode language: HTML, XML (xml)

Move over image

/* START move wrapped title, meta, and text up over the image */
.pa-blog-text {
	position: absolute;
	top: 50%;
	left: 50%;
	transform: translate(-50%, -50%);
	width: 100%;
	padding: 30px;
	z-index: 1;
}
.et_pb_blog_grid article {
	position: relative;
}
.et_pb_blog_grid .et_pb_post {
	padding: 0px;
}
.et_pb_image_container {
	margin: 0;
}
.et_pb_post .entry-featured-image-url {
	margin: 0;
}
.et_pb_blog_grid .entry-featured-image-url::before {
	content: '';
	position: absolute;
	width: 100%;
	height: 100%;
	background-color: rgba(0, 0, 0, 0.5);
}
/* END move wrapped title, meta, and text up over the image */Code language: CSS (css)