For paragraph-to-paragraph translation, you should use Word's table feature on the Insert ribbon instead of the "columns" button on the Layout ribbon. In a copy of the original document, select the text between two headings. On the Insert > Table menu, click Convert Text to Table. In the dialog that opens, go to the "Separate text at" section and click the Paragraphs option button; at the top, the number of rows should automatically equal the number of paragraphs you selected. (Note: don't try to change the number of columns in this dialog.) Click OK.
The inserted table has one column, with each paragraph in a separate cell. The Layout tab for tables appears on the far right above the ribbon. On that tab, in the Rows & Columns group, click the Insert Right button. The table will now have two columns, with empty cells in the column on the right. You can write the translations in that empty column, and each paragraph will start at the same height as its corresponding paragraph in the left column.
You could use the Borders menu on the Table Design ribbon to make the table borders invisible, but the quick way is to press Ctrl+Alt+U while the cursor is in the table. It's a good idea to keep the gridlines visible (turn on the View Gridlines button on the Layout ribbon) while you edit the document; these lines won't print.
Much more about tables can be found at http://addbalance.com/usersguide/tables.htm.