I would set up a German language site and an English language site, and put a clear and easy path between them. That way you can target English terms on one, and German on the other (using the proper German characters). If someone who speaks German uses the English terms, they can easily navigate to the equivalent content on your other site.
I would strongly urge you to use a .de TLD (top level domain) for the German content, since country-specific TLD's get better rankings in the search engines (especially Google), and you can use the respective search engine webmaster tools to specify market, language etc. Second choice would be a
www.mydomain.com/de/ section of your .com domain (note that Google now lets you specify country/language targeting for directories). Subdomains would be my third choice -- none of the advantages of a .de domain and you diffuse your linking by adding another domain.
Another thing to consider is searchers who use a mix of English and German. Here you may need to include some English terms that are commonly mixed this way in your German content.