Index: src/wp-includes/js/tinymce/plugins/wpeditimage/plugin.js
===================================================================
--- src/wp-includes/js/tinymce/plugins/wpeditimage/plugin.js	(revision 36969)
+++ src/wp-includes/js/tinymce/plugins/wpeditimage/plugin.js	(working copy)
@@ -1,6 +1,6 @@
 /* global tinymce */
 tinymce.PluginManager.add( 'wpeditimage', function( editor ) {
-	var toolbar, serializer, touchOnImage,
+	var toolbar, serializer, touchOnImage, letPasteInCaption,
 		each = tinymce.each,
 		trim = tinymce.trim,
 		iOS = tinymce.Env.iOS;
@@ -853,19 +853,56 @@
 				}
 			});
 		}
-    });
+	});
 
+	editor.on( 'pastePostProcess', function( event ) {
+		var element, captionNode = editor.dom.getParent( editor.selection.getNode(), 'dd.wp-caption-dd' );
+
+		if ( captionNode ) {
+			var walker = new tinymce.dom.TreeWalker( event.node, event.node );
+
+			while ( element = walker.next() ) {
+				if ( editor.dom.isBlock( element ) ) {
+					// Mark nodes for removal. Can't remove them now as that stops the walker.
+					editor.dom.setAttrib( element, 'data-wp-removeme', 'true' );
+				} else if ( element.nodeName === 'IMG' || element.nodeName === 'AUDIO' || element.nodeName === 'VIDEO' || element.nodeName === 'svg' ) {
+					// Can't be pasted in the image caption. Will be inserted in a new paragraph under it.
+					return;
+				}
+			}
+
+			editor.$( '[data-wp-removeme]', event.node ).each( function( i, node ) {
+				// Insert <br> where the blocks used to be. Otherwise longer text runs together and looks bad.
+				editor.dom.insertAfter( editor.dom.create( 'br' ), node );
+				editor.dom.remove( node, true );
+			});
+
+			// Pasted HTML is cleaned up for inserting in the caption.
+			letPasteInCaption = true;
+		}
+	});
+
 	editor.on( 'BeforeExecCommand', function( event ) {
-		var node, p, DL, align, replacement,
+		var node, p, DL, align, replacement, captionParent,
 			cmd = event.command,
 			dom = editor.dom;
 
 		if ( cmd === 'mceInsertContent' ) {
-			// When inserting content, if the caret is inside a caption create new paragraph under
-			// and move the caret there
-			if ( node = dom.getParent( editor.selection.getNode(), 'div.mceTemp' ) ) {
+			node = editor.selection.getNode();
+			captionParent = dom.getParent( node, 'div.mceTemp' );
+
+			if ( captionParent ) {
+				if ( letPasteInCaption && dom.getParent( node, 'dd.wp-caption-dd' ) && event.value.data && event.value.data.paste ) {
+					letPasteInCaption = false;
+					// We are in the caption element, and in 'paste' context,
+					// and the pasted HTML was cleaned up on 'pastePostProcess' above.
+					// Let it be pasted!
+					return;
+				}
+
+				// Make new paragraph under the caption parent element and move the caret there.
 				p = dom.create( 'p' );
-				dom.insertAfter( p, node );
+				dom.insertAfter( p, captionParent );
 				editor.selection.setCursorLocation( p, 0 );
 				editor.nodeChanged();
 			}