Since you do not want to use runat="server" then you need to make use of a HiddenField and copy the contents of DIV to it before PostBack and then access the HiddenField on server side.
HTML
<form id="form1" runat="server">
<div id="dvContent1">
<span style="font-family: arial; font-size: 10pt">My name is <span style="color: Red">
Mudassar Khan</span></span>
</div>
<input type="hidden" id="div_content" name="div_content" />
<asp:Button Text="Submit" runat="server" OnClientClick="SaveToHidden()" OnClick="GetDIVContents" />
<script type ="text/javascript">
function SaveToHidden() {
var content = document.getElementById("dvContent1").innerHTML;
document.getElementById("div_content").value = content;
}
</script>
</form>
Code
protected void GetDIVContents(object sender, EventArgs e)
{
string content = Request.Form["div_content"];
}
And if you receive an error refer the article