It isn't possible. If you try by overriding TextBox and calling SetStyle(ControlStyles.UserPaint, true) in the constructor so you can override OnPaintBackground and draw the image, you'll be in for several rude surprises. Falling back to legacy rendering mode is just one of them.
TextBox dates from the very early days of Windows, back when it still had to run on 386SUX hardware. One particular crime it commits to work reasonably on such limited hardware was to draw itself without using the WM_PAINT event. This destroys the background image.
There's a project at CodeProject.com that provides one. I cannot recommend it.
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