The syntax of your IIF function is wrong.
IIF Function

Also watch: Null

IIF(FieldName = "" or IsNull(FieldName), Value If True, Value If False)

Thanks, Kevin.  My bigger question is what goes in the ??? place?  If InvoiceNumberHigh is blank, and InvoiceNumberLow is blank, what is the syntax to make the return the equivalent of "*" ?

Check out the Combining Names video.  You are going to need a nested IIF() statement.

IIF(FieldName1 = "" or IsNull(FieldName1), Value If True, IIF(FieldName2 = "" or IsNull(FieldName2),Value If True,Value if Neither are True)

Hi Tom, you need both a lower limit and upper limit to filter anything.  If either is blank, nothing should be or could be done.  To answer your question, there is no "*" option in that situation.  So if the user doesn't provide both lower and upper limits, you need to have the user do so before the IIf() function is run.  In my old job, when the user typed in either a lower or upper limit, the other limit would be automatically filled in as the same value (see picture below), so both fields would not be blank, and would guarantee to return at least one record, if it existed.  And the user could enter a different upper or lower limit if he wanted to.  If the user didn't enter anything, nothing would be done.  This is really about user interface design, and you can do it differently if you want.  This is not something a single IIf() function can do, so you may need VBA.

Thank you, Kevin.  That's not the answer I wanted, but you did answer my question.  I'll add default values to my form until I get the opportunity to research a VBA solution.

Tom if you take a look at the Search Form 2.0 video, Richard shows this with dates and credit limit.  It is a little more involved writing the SQL but by having the MinSearch and MaxSearch I think that will help you achieve what you are trying to do.
As Kevin indicated it isn't really possible in a regular query.