> I have a strange case that https URLs are not
> downloaded via proxy.

Is your proxy supporting https GET requests ? httrack is currently unable to
use the pass-through feature (CONNECT) and rely on direct GET commands in
clear text.

Can you try this on a console (if you can access to a unix-style console) (one
single line):

echo -en "GET <https://www.google.com/intl/en_ALL/images/logo.gif>
HTTP/1.0\r\nHost: www.google.com\r\nProxy-Authorization: Basic
ENCODED_RESULT\r\n\r\n" | nc ip_of_squid_proxy 8080

With ENCODED_RESULT being the base64 user:pass form you can compute here for
example:
<http://tuxgraphics.org/toolbox/base64-javascript.html>

If you get something like:
..
The following error was encountered:
..
Unsupported Request Method and Protocol

Then your proxy is not allowing direct GET in https.