% !TEX TS-program = pdflatexmk
% To use the line above, make sure that the pdflatexmk engine is moved
% from the Inactive folder to the Engines folder inside ~/Library/TeXShop
% This will automatically run bibtex on each of the bbl files created by 
% bibunits
\documentclass[]{report}
\usepackage{lipsum}
%\usepackage{natbib}
\usepackage{titlesec}
\usepackage{bibunits}
\begin{document}
\begin{center}VITA\end{center}
\begin{bibunit}[IEEEtran]
% redefine chapter within this bibunit to not eject a page
\makeatletter
\renewcommand\chapter{\par%
  \thispagestyle{plain}%
  \global\@topnum\z@
  \@afterindentfalse
  \secdef\@chapter\@schapter}
\makeatother
% redefine \chapter to your vita heading style
\titleformat{\chapter}[display] 
{\normalfont\itshape}{\chaptertitlename\ \thechapter}{0pt}{}
\titlespacing*{\chapter} {0pt}{3.5ex plus 1ex minus .2ex}{2.3ex plus .2ex} 
\renewcommand{\bibname}{JOURNAL PUBLICATIONS}

\nocite{*}
Your vita here
\putbib[journal] % your journal bibfile
\end{bibunit}
% redefine \chapter back to normal
\titleformat{\chapter}[display] 
{\normalfont\huge\bfseries}{\chaptertitlename\ \thechapter}{20pt}{\Huge} 

\chapter{A chapter}
\begin{bibunit}[IEEEtran]
This is a citation.

\putbib[] % insert the name of your thesis bib file here

\end{bibunit}
\end{document}