e-Business function has seen many configurations - separate function, within the IT Organization, within the marketing organization and everything in between.
The problem starts with a clear understanding of e-Business - what is it? Some take it to be a different kind of it; some as a new channel and some others as a new business. This article argues for differentiated talent for "digital marketing." This is fine coming from recruitment firm but a practitioner would have made the same argument for "e-Business" because it should not be split into "marketing" and "it" etc.
In any event, the discussion is interesting and worth a read!