When you submit the form and instigate the request what your asp.net code is doing is sending a response. When you're doing a normal page, asp.net will generate html from your controls and write that response as text\html and that's the response, it appears in the browser. When you set your own content type as a zip file and use transmitfile then you're taking over from asp.net and sending your own custom response, so the browser is offered to download the file. A request can only have one response....you can't send a file *and* send html. If you want one request to have two responses (a download and html) then you'll need to employ some trickery.
A common technique is to send your page as normal with your text, and in that page put a hidden iframe with the src pointing to a page that does the transmitfile. That way they see the message, and then get the file download prompt.
<iframe src="download.aspx?file=filenametodownload" width="1" height="1" style="display:none;"></iframe>
Your download.aspx will then read the filename and instigate the transmitfile.