How do I get my iPhone to give both audio and vibrate alerts when wearing my Apple Watch?

As BobHarris correctly points out you can't and that's by design.

Read this link about Notifications on Apple Watch --> Notifications on your Apple Watch - Apple Support

The very first section of this link from Apple says the following:

"Notifications go to either your Apple Watch or iPhone, but not both."

You don't

Apple Watch Feedback

https://www.apple.com/feedback/watch.html

Make sure you click on the Feedback link above, and tell Apple. The volunteers here in this forum have no control of what Apple does.