I was very surprised to find out, but iTunes actually lets you access a podcast protected through the regular HTTP basic or digest authentication.

When you subscribe to such a feed iTunes will ask you for a username and a password.

Try subscribing to this feed in iTunes, for example: private feed

So if your server lets you setup your own HTTP protection through .htaccess or what not, you can password protect your podcast. If you combine this with SSL, you have a pretty solid protection mechanism, but for just family stuff I would think that the digest authentication is good enough. Just don't use basic authentication because that will send the password over in cleartext.

More on this topic in my blog