OK, I see what you mean. The only way I can think of is to use JavaScript to hide it when you are on the Home page or Contact Us
Try pasting this at the bottom of the navbar template
Code:
<script>
if(fetch_object("tab_ntk2_394").className == "selected" || fetch_object("tab_mte4_890").className == "selected") {
fetch_object("globalsearch").style.display = "none";
fetch_object("navbar").style.height = "26px";
}
</script>