According to SOWPODS (the combination of Scrabble dictionaries used around the world) there are 34 words with the pattern ----H-N-E-. That is, ten letter words with 5th letter H and 7th letter N and 9th letter E. In alphabetical order, they are:
antihunter
apophonies
bacchantes
backhanded
backhander
barehanded
bellhanger
diaphonies
epiphanies
evenhanded
forehanded
freehanded
hardhanded
headhunted
headhunter
ironhanded
keeshonden
manchineel
merchanted
minehunter
mischanced
mischances
mischannel
mischanter
molehunter
mumchances
openhanded
outthanked
overhanded
overhunted
snaphances
subchanter
symphonies
trochanter