I'm trying to write a script that uses a HTTP proxy to post information on a https site and then read the information sent back, Is it possible? Maybe I need a DLL to do this?

Yap.. That is possible.. You need ssl tunnel program like stunnel.. Check the examples of ussing on their site..
Also to see how your browser works with a proxy you can use a sniffer like Iris.. Often that will save you to read the boring RFC docs..

Okay, I'll try that. Thanks for your help

You can use a COM object called XMLHTTP for that. This script will request a page and return the HTTP response headers:

• alias getpage {
  .comopen gp Microsoft.XMLHTTP
  !.echo -q $com(gp,Open,1,bstr,Get,bstr,$1,bool,false)
  !.echo -q $com(gp,Send,1)
  !.echo -q $com(gp,GetAllResponseHeaders,1)
  var %result = $com(gp).result
  .comclose gp
  return %result
  }

To test it, try: //echo -a $getpage(http://www.yahoo.com)

Edit: Keep in mind that due to mIRC limitations, you cannot use this object to retrieve a webpage body if it's longer than ~900 characters.

mIRC COM Tutorial
Article from 4GuysFromRolla
MSDN Object Reference

That's exactly what I was looking for. What about proxy support though? Do I have to script something else to get it to work with a proxy? Or does it use the proxy specified in Internet Explorer settings?

It uses IE's engine, so it follows its proxy settings too

Fantastic, thanks a lot!

Oh, Also, What would I search for if I wanted more commands (Open, GetAllResponseHeaders, etc) so that maybe I could use this to display an entire webpage?

Right after $com(gp,Send,1) you can call $com(gp,responseText,2) and $com(gp).result will hold the entire page contents.

For more methods and properties, see the MSDN reference