What is DataHandler? Is it a class which origins your mind - or is it something you use just for convenience, because it was there?
Whenever you're challenged with interop questions, it is good to stick with what web-services really ment to offer: Transporting data from one end of the wire to the other end.
So maybe DataHandler has a member that represents the connection to a database - you cannot serialize things like that.
Identify the parts your really need, write your own, custom class - the bean-style way, then there should be no problems with axis and .net.
If this post didn't help, please be a bit more specific.