Unfortunately, when you change the background color while writing an email, it changes the background color for the ENTIRE EMAIL, not just the text that you have highlighted.

See here for various solutions.

The best solution, IMHO, is to edit your email in another editor (Abiword, for example), and apply your styling there. Then, copy and paste it into Thunderbird, and the styling should show up there.

simple HTML editors — browser-based

simple HTML editors — Linux-based