diff --git a/packages/block-library/src/cover/style.scss b/packages/block-library/src/cover/style.scss
index c6f358d577c1f5..8ac60265306036 100644
--- a/packages/block-library/src/cover/style.scss
+++ b/packages/block-library/src/cover/style.scss
@@ -37,7 +37,6 @@
 	h2,
 	.wp-block-cover-image-text,
 	.wp-block-cover-text {
-		color: $white;
 		font-size: 2em;
 		line-height: 1.25;
 		z-index: 1;
@@ -45,7 +44,12 @@
 		max-width: $content-width;
 		padding: $block-padding;
 		text-align: center;
+	}
 
+	h2:not(.has-text-color),
+	.wp-block-cover-image-text,
+	.wp-block-cover-text {
+		color: $white;
 		a,
 		a:hover,
 		a:focus,
@@ -130,7 +134,9 @@
 	h5,
 	h6,
 	.wp-block-subhead {
-		color: inherit;
+		&:not(.has-text-color) {
+			color: inherit;
+		}
 	}
 }