There is a HTML based readme file included with nHTMLn.DLL - you will need to read that and understand how to call DLL's in mIRC scripts. I have a simple script below which may help and can be used as a guide. Place the DLL in the root directory in this case.
Code:
ie {
  window -aek0p @Browser 0 0 800 600
  var %bs.bs $dll(nHTMLn.dll,attach,$window(@Browser).hwnd) 
  var %bd.bd $dll(nHTMLn.dll,navigate,http://iserv.com.au/)
}
Place that in your aliases.ini file on a new line and make sure there's no other aliases beginning with the same command. Then just change the URL to whatever your home page is. The code under goes in a remotes file:
Code:
ON *:INPUT:@Browser: {
  var %bs.bs $dll(Scripts\TCOM\nHTMLn.dll,attach,$window(@Browser).hwnd) 
  var %bd.bd $dll(Scripts\TCOM\nHTMLn.dll,navigate,$1)
  if (http:// isin $1) {
    editbox @Browser $1
  }
  if (http !isin $1 && .htm !isin $1 && .asp !isin $1 && .cfm !isin $1 && .pl !isin $1 &&.php !isin $1) {
    editbox @Browser http:// $+ $1 $+ /
  }
  if (http isin $1 && .htm !isin $1 && .asp !isin $1 && .cfm !isin $1 && .pl !isin $1 &&.php !isin $1) {
    editbox @Browser $1
  }
  if (http !isin $1 && .htm isin $1 || .asp isin $1 || .cfm isin $1 || .pl isin $1 || .php isin $1) {
    editbox @Browser http:// $+ $1 $+ /
  }
  if (http isin $1 && .htm isin $1 || .asp isin $1 || .cfm isin $1 || .pl isin $1 || .php isin $1) {
    editbox @Browser $1
  }
}
This lets you navigate to a new site with a normal mIRC edit box. It has some minor error management to allow URL's you go to to be displayed correctly, as per IE. Improve on it if you will, it's not perfect but does the job.

NOTES: The local variables merely silence the messages sent to Status WIndow by the DLL which confirm success or an error, if you want to see the msgs then just delete the "var %*" bit from both lines.

Only thing I don't like is the editbox cuts off the bottom 10pixels of a webpage which can mean the bottom arrow in the scrollbar can be 'hidden' behind the editbox but that's not big deal for me at the moment.