Manage InputBox method reference entry
I'm not sure where you got xlInputReference from, or 16. According to the MSDN page you linked, the correct type for a reference input is 8. 

I'm not sure I like your approach. You only need this for range inputs. Personally, I would handle this (prompting for range inputs) by asking for a cell reference (as text) then converting that text into a range object separately (with appropriate error handling).

But, to take your current approach:



As it stands, I've got very little that I can see improvements for.  

You shouldn't use Integer. It is completely deprecated. Use Long instead.  

Your method name isn't great and breaks convention (that Metohd names use PascalCase). I would use something like HandleInputBox.

Since yes, you can have compound return types but obviously, trying to return some combination of object + text + number is going to fail, you probably want to check for it:

If dataType Mod 16 &gt;= 8 Then
    If dataType &lt;&gt; 8 Then
    '/ Compound of 8 with other values
        '/ Error handling
    Else
        On Error GoTo InputCancelled
        Set mjInputBox = Application.InputBox(prompt:=prompt, Title:=Title, Default:=Default, Type:=dataType)
        On Error GoTo 0
    End If
Else
    mjInputBox = Application.InputBox(prompt:=prompt, Title:=Title, Default:=Default, Type:=dataType)
End If


You should probably implement all the other optional arguments for Application.InputBox() as well since you only have to pass them through.

Other than that, I have nothing to critique. The code is good.