HCM  p.  14 says:   "A miagkii znak (prime) is placed between two   letters  representing  two  distinct  consonants  when   the  combination might otherwise be  read  as  a  digraph."  Thus,  the  miagkii znak can appear only between "t" and  "s" (tav-samekh with  no  vowel between) to  avoid confusion with  "ts" (tsade), between  "s"  and  "h" (samekh-he with no vowel between) to avoid confusion  with "sh" (shin), and between "k" and  "h" (kaf-he with  no vowel between; ) to avoid confusion with "kh" (khaf).  If  "khaf"  is followed  by  "he,"   there's no problem that needs  to  be resolved with  the  use  of   miagkii znak:   the combination "khh"  is  not ambiguous.
 

It  can never occur between "t" and "h" (tav-he with no vowel  between), since  "th"  is  never  read  as  a digraph (two letters  representing a single sound) in Hebrew romanization.

Examples:
     hithavutah (inferior dot under the "v")--no miagkii znak
     Hildes'haimer (miagkii znak between "s" and "h")
     Kalk'haim (miagkii znak between "kh" and "h")