A GtkCombo has an associated entry which can be accessed using the following expression:
GTK_COMBO(combo_widget)->entry
If you don't want the user to be able to modify the content of this entry, you can use the gtk_entry_set_editable() function:
void gtk_entry_set_editable(GtkEntry *entry, gboolean editable);
Set the editable parameter to FALSE to disable typing into the entry.