Not really. There are two ways to communicate with mIRC, DDE and the SendMessage() API, but neither of them is available in JScript.
If you want and know how, you can write an ActiveX DLL that uses either of the mentioned ways, and this will give you complete control over mIRC. See the help file for technical info.
Meanwhile, here is a partial solution that will let you throw commands at mIRC (I'm saying "throw" because you can't tell whether the command arrives and when it completes).
First, download Zruntime DLL
and place it in the same directory as your .HTA file.
Then, put something like this in your source code:
oWSH = new ActiveXObject('WScript.Shell');
alert('Fatal error: ' + e.description);
rundll = 'rundll32 Zruntime.dll,DDEmIRC mIRC,' + cmd;
<INPUT type="text" size="55" id="oSendBox"
value="/echo -s moo">
value="Send to mIRC">
HTH, and sorry that I can't help any further.