Hmmm this could quickly turn into Pandora's Box for you. What I would suggest first is to examine the .VBS file and see if you can turn it into an ASP page instead. If you can then go that route.
If it can't then you will need to use something like:
set wshell = server.CreateObject("WScript.Shell")
strCommand = "cmd.exe /c c:\myCode.vbs
set wshell = nothing
Here are a few of the caveats:
By default the XXX_IUSR account does not have rights to execute this command (for good reason) so you will need to elevate that users permission (or whatever user you have configured that your website runs under)
If you are using IIS 6+ you need to assign a user for the subweb and give that user permissions to execute wscript and cmd.
I would definately not advise doing this since it opens your server up to malcious attacks.
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