Presuming that your hoster has enabled SSI's and delegated Read/Write permissions for handler mappings then this should work:
<configuration>
<system.webServer>
<handlers>
<add name="SSINC-html"
path="*.html"
verb="*"
modules="ServerSideIncludeModule"
resourceType="File"
requireAccess="Script" />
</handlers>
</system.webServer>
</configuration>
Whilst we're on the topic, Robert McMurray (MSFT IIS staffer) has a fairly recent refresher blog post all about SSI's here: