Response to Graham Skan: I searched MS Word help, Herb Tyson's Word 2007 Bible, and I Googled "vba word linked styles". Nothing helped with my particular problem.
Since then, I found a solution:
a. Specify a new character style named "Italics" or whatever name you want. Define its formatting as italics.
b. Instead of simply selecting text and pressing Ctrl + I to italicize the selected text, apply the new style to the selection. You can have VBA do that too, as long as you have previously created the character style.
c. When you then apply a new paragraph style to the paragraph, it retains the character styles in the paragraph.
The only problem I see with that solution is how can one make a new character style in MS Word 2007? It has a bug (a feature?) that will not let you make a new character style in the Apply Styles window where you normally make new paragraph styles. (The character style choice is deactivated.) Instead, to make a new character style, you have to go to the Home tab and in the "Styles" section, you click on the little button in the lower right corner.
That opens the "Styles" window at the bottom of which are three buttons. The leftmost of those three buttons is the "New Style" button. If you click on that, you see the same dialog box you see in the Apply Styles window, but here the character style choice is no longer deactivated.
Thanks to you and JOrzech for your help. Without your comments, I probably would not have found the solution.
--j.r.a.