Well it might be a long way around the problem, but I would say your best bet would be to copy that text as "plain text" before you make the HTML document out of it.  To do this, you could copy and paste it into Notepad first, and then from there clean up anything that doesn't look right - and then copy and paste it from Notepad into Dreamweaver.

That way you would not be copying the font styles as well as the text itself.  Of course, if somebody has a simple solution to the problem - I would hear them out as well. 

Is it an unusual font that is instead displaying as Times New Roman? Is it installed on your pc?

In addition to Mitch's suggestions:

Does DW have an "import file" command that will work with Word files? Try that after saving the .doc as .htm.

And also maybe try it after saving the Word files as .DOC, so DW does the conversion rather than Word.

You can also open the DOC in Word and copy the full text to the clipboard. Then paste it into your page in DW in Design view. If there are various paste options, experiment.

These are the methods I've used in FrontPage, but I assume DW has a parallel feature set. The basic idea is that there are several ways to get text from Word to a web page, and they can give different results.

When all else fails, I use Mitch's method, and that always works, as much trouble as it is.

Set the Font in DW first, open a new page. Go to Modify menu> page properties, you will see the fonts there.

Do not convert Word to HTML. Word HTML code is horrible. Use the import word command from the File menu.  I use DW MX 2004, it may be slightly different in other versions.