A script invoking Firefox on Cygwin.

firefox-open.sh

#! /bin/sh

# Confirm that the script is invoked from a Windows session,
# not a SSH session.
if [ -z "$SESSIONNAME" ] ; then
  exit;
fi

alias firefox='/cygdrive/c/Program\ Files\ \(x86\)/Mozilla\ Firefox/firefox.exe'

if (echo $1 | egrep --silent "^file:///") then
    # the file exists in the local machine
    PATH_OF_LOCAL_FILE=`echo $1 | sed 's/file:\/\///'`;
    URL=file:///`cygpath --mixed $PATH_OF_LOCAL_FILE `
elif (echo $1 | egrep --silent "^file://[^/]") then
    # the file exists in the remote machine on network
    PATH_OF_REMOTE_FILE=`echo $1 | sed 's/file://'`;
    URL=file:///`cygpath --mixed $PATH_OF_REMOTE_FILE `
else
    URL=$1
fi

#firefox -remote 'OpenURL('$URL',new-tab)'

firefox -new-tab $URL &

Or perhaps just: cygstart $URL