Unfortunately this is not possible in Word. But it can be done in PowerPoint, so I suggested to use that to his advantage.
Here's how:
Open your Word file. Go to Insert - Object (text group) - Object - choose Microsoft PowerPoint slide.
Adjust the height and width of the object window so that it fits your Word margins.
Select the placeholders and delete them or apply the empty slide layout.
Go to Insert - Table - drag the number of columns/rows you want and click to make your table.
Adjust the table so that it fits the object window.
Now, on the contextual Design tab, in the styles for tables group, click the first table style of the second row (should indicate No style, table grid).
Now click on the Fill button in the same group, choose Table background, click Picture, navigate to your picture, select it and click Insert.
Now the table will have a background. The advantage of using an object is that the table can easily be edited and extra rows and columns can be added without loosing the background. To edit, simply double click the object and edit away. To make the text readable you may have to adjust the colour of the font.
Once the table is finished just click next to it and it will seem as if it has been made in Word.
