There is only one file type that uses the .MSHI extension:
Microsoft Help Index File
Help documentation file created in the MS Help Viewer 1.x index format; saves a topical index that is used for browsing and searching the help documentation; used by software developers when authoring the help topics for their software titles.
MSHI files are used for indexing the content in .MSHC help container files. When an MSHI file exists, it is deployed with the corresponding MSHC file within a signed .CAB archive.
NOTE: MS Help Viewer 1.x replaces the MS Help 2.x (.HXS) and MS Help 1.x (.CHM) formats.
Updated: July 10, 2013