Business Architecture is part of Enterprise Architecture

Enterprise Architecture does by definition include Business Architecture. Any other view is now rather out of date. 

Enterprise Architecture should include several domains: 

•  Strategy 
• Business Architecture 
• Information/Data Architecture 
• Application Architecture 
• Infrastructure Architecture

In addition there are other sub-domains for Process Improvement, Governance, Audit, Security etc. 

All EA frameworks including Zachman, Archimate, IAF and TOGAF 9 recognise these distinct domains in some form. 

TOGAF 9 is increasing mature and the image at http://tinyurl.com/btxqga 
is a good baseline for understanding the various domains. 

Of course over the history of the maturing of the Enterprise Architecture discipline, it was nearly always the case that Architects came out of the IT function.

IT trained staff are more likely to be good modellers and think in rational formal ways necessary to produce good Architecture models.

Business staff on the other hand like to own their business models and have been less precise and formal about how they modelled what they do.

This is improving of late with BPMN and BMM models becoming more acceptable for business focused staff to use.

The Enterprise Architect is also increasingly becoming a Strategy & Architecture discipline and an Enterprise Architecture (as opposed to a Solution Architect) likely not to have an IT background. Many are from a Business Analysis, Programme Management, Portfolio Management background.

The ideal EA team today will have a mixture of all kinds off staff from different disciplines and will not report to the IT function.

EA is a corporate level function and not just a Business or IT function.