There are numerous ways to do this:
You could simply use different colored text, or perhaps a combination of the following will yield the desired something to your liking.
Here is an example of using the mdframed package to highlight the different sections:

You could use adjustwidth environment from the changepage package to visually separate the two paragraphs:

You could use the changebar package:

If your paragraphs are not too large you could use the solution from Mark portions of text without affecting spacing to make the begin and end of the paragraphs:

In case you want to have solutions which do not require using separate paragraphs,
here is a version comparable to the mdframed, which uses the solution from Cool Text Highlighting in LaTeX to provide highlighting which appears manually generated:

Code: mdframed:
\documentclass[border=5pt]{standalone}
\usepackage{xcolor}
\usepackage{mdframed}
\usepackage{lipsum}
\newmdenv[
backgroundcolor=yellow!10,
rightline=false,
leftline=false,
topline=false,
bottomline=false,
innertopmargin=1pt,
innerbottommargin=1pt,
innerleftmargin=0,
innerrightmargin=0,
]{VoiceA}
\newmdenv[
backgroundcolor=gray!10,
rightline=false,
leftline=false,
topline=false,
bottomline=false,
innertopmargin=1pt,
innerbottommargin=1pt,
innerleftmargin=0,
innerrightmargin=0,
]{VoiceB}
\begin{document}
\begin{VoiceA}
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Phasellus ut elit ipsum.
In massa metus, suscipit vel semper in, sodales sed risus.
Aliquam gravida ultricies sollicitudin.
\end{VoiceA}
\begin{VoiceB}
Vivamus et sem velit.
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aliquam erat volutpat.
Sed rhoncus neque a orci vulputate ut elementum dui ornare.
\end{VoiceB}
\begin{VoiceA}
Nulla id magna metus. Integer lacus dolor, tempus ac sodales
eu, blandit nec ligula.
Etiam quis arcu ac nisi lobortis ultricies quis in dolor.
Quisque lobortis magna arcu.
\end{VoiceA}
\end{document}
Code: adjustwidth:
\documentclass[border=5pt]{standalone}
\usepackage{lipsum}
\usepackage{changepage}
\newenvironment{VoiceA}{%
\begin{adjustwidth}{0pt}{1.0cm}%
}{%
\end{adjustwidth}%
}
\newenvironment{VoiceB}{%
\begin{adjustwidth}{1.0cm}{0pt}%
}{%
\end{adjustwidth}%
}
\begin{document}
\begin{VoiceA}
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Phasellus ut elit ipsum.
In massa metus, suscipit vel semper in, sodales sed risus.
Aliquam gravida ultricies sollicitudin.
\end{VoiceA}
\begin{VoiceB}
Vivamus et sem velit.
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aliquam erat volutpat.
Sed rhoncus neque a orci vulputate ut elementum dui ornare.
\end{VoiceB}
\begin{VoiceA}
Nulla id magna metus. Integer lacus dolor, tempus ac sodales
eu, blandit nec ligula.
Etiam quis arcu ac nisi lobortis ultricies quis in dolor.
Quisque lobortis magna arcu.
\end{VoiceA}
\end{document}
Code: changebar:
\documentclass{article}
\usepackage{lipsum}
\usepackage[xcolor,outerbars]{changebar}
\setlength\changebarsep{5pt}
\newenvironment{VoiceA}{%
\cbcolor{red}%
\par%
\cbstart%
}{%
%
\cbend%
}
\newenvironment{VoiceB}{%
\cbcolor{white}% gets cluttered if both have changebars
\par%
\cbstart%
}{%
\cbend%
}
\begin{document}
\begin{VoiceA}
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Phasellus ut elit ipsum.
In massa metus, suscipit vel semper in, sodales sed risus.
Aliquam gravida ultricies sollicitudin.
\end{VoiceA}
\begin{VoiceB}
Vivamus et sem velit.
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aliquam erat volutpat.
Sed rhoncus neque a orci vulputate ut elementum dui ornare.
\end{VoiceB}
\begin{VoiceA}
Nulla id magna metus. Integer lacus dolor, tempus ac sodales
eu, blandit nec ligula.
Etiam quis arcu ac nisi lobortis ultricies quis in dolor.
Quisque lobortis magna arcu.
\end{VoiceA}
\end{document}
Code: Paragraph Markers:
\documentclass[border=5pt]{standalone}
\usepackage{environ}
\usepackage{tikz}
\usepackage{mathabx}
% https://tex.stackexchange.com/questions/24174/mark-portions-of-text-without-affecting-spacing
\DeclareRobustCommand{\MarkStart}[1]{{%
\setbox0=\llap{\raisebox{5pt}{\color{#1}$\Rsh$\kern-6pt}}%
\ht0=0pt \dp0=0pt \leavevmode\box0
}}
\DeclareRobustCommand{\MarkEnd}[1]{{%
\setbox0=\rlap{\raisebox{5pt}{\color{#1}\kern-6pt$\Lsh$}}%
\ht0=0pt \dp0=0pt \leavevmode\box0
}}
\newcommand*{\Mark}[1]{\MarkStart#1\MarkEnd}
\NewEnviron{VoiceA}{\par\MarkStart{red}\BODY\MarkEnd{red}}
\NewEnviron{VoiceB}{\par\MarkStart{blue}\BODY\MarkEnd{blue}}
\begin{document}
\begin{VoiceA}
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Phasellus ut elit ipsum.
In massa metus, suscipit vel semper in, sodales sed risus.
Aliquam gravida ultricies sollicitudin.
\end{VoiceA}
\begin{VoiceB}
Vivamus et sem velit.
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aliquam erat volutpat.
Sed rhoncus neque a orci vulputate ut elementum dui ornare.
\end{VoiceB}
\begin{VoiceA}
Nulla id magna metus. Integer lacus dolor, tempus ac sodales
eu, blandit nec ligula.
Etiam quis arcu ac nisi lobortis ultricies quis in dolor.
Quisque lobortis magna arcu.
\end{VoiceA}
\end{document}
Code: Cool Highlighting:
\documentclass[border=5pt]{standalone}
\usepackage{soul}
\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{decorations.pathmorphing}
% https://tex.stackexchange.com/questions/5959/cool-text-highlighting-in-latex
\makeatletter
\newcommand{\defhighlighter}[3][]{%
\tikzset{every highlighter/.style={color=#2, fill opacity=#3, #1}}%
}
\defhighlighter{yellow}{.3}
\newcommand{\highlight@DoHighlight}{
\fill [ decoration = {random steps, amplitude=1pt, segment length=55pt}
, outer sep = -15pt, inner sep = 0pt, decorate
, every highlighter, this highlighter ]
($(begin highlight)+(0,8pt)$) rectangle ($(end highlight)+(0,-3pt)$) ;
}
\newcommand{\highlight@BeginHighlight}{
\coordinate (begin highlight) at (0,0) ;
}
\newcommand{\highlight@EndHighlight}{
\coordinate (end highlight) at (0,0) ;
}
\newdimen\highlight@previous
\newdimen\highlight@current
\DeclareRobustCommand*\highlight[1][]{%
\tikzset{this highlighter/.style={#1}}%
\SOUL@setup
%
\def\SOUL@preamble{%
\begin{tikzpicture}[overlay, remember picture]
\highlight@BeginHighlight
\highlight@EndHighlight
\end{tikzpicture}%
}%
%
\def\SOUL@postamble{%
\begin{tikzpicture}[overlay, remember picture]
\highlight@EndHighlight
\highlight@DoHighlight
\end{tikzpicture}%
}%
%
\def\SOUL@everyhyphen{%
\discretionary{%
\SOUL@setkern\SOUL@hyphkern
\SOUL@sethyphenchar
\tikz[overlay, remember picture] \highlight@EndHighlight ;%
}{%
}{%
\SOUL@setkern\SOUL@charkern
}%
}%
%
\def\SOUL@everyexhyphen##1{%
\SOUL@setkern\SOUL@hyphkern
\hbox{##1}%
\discretionary{%
\tikz[overlay, remember picture] \highlight@EndHighlight ;%
}{%
}{%
\SOUL@setkern\SOUL@charkern
}%
}%
%
\def\SOUL@everysyllable{%
\begin{tikzpicture}[overlay, remember picture]
\path let \p0 = (begin highlight), \p1 = (0,0) in \pgfextra
\global\highlight@previous=\y0
\global\highlight@current =\y1
\endpgfextra (0,0) ;
\ifdim\highlight@current < \highlight@previous
\highlight@DoHighlight
\highlight@BeginHighlight
\fi
\end{tikzpicture}%
\the\SOUL@syllable
\tikz[overlay, remember picture] \highlight@EndHighlight ;%
}%
\SOUL@
}
\makeatother
\begin{document}
\highlight[yellow]{
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Phasellus ut elit ipsum.
In massa metus, suscipit vel semper in, sodales sed risus.
Aliquam gravida ultricies sollicitudin.
}
\highlight[gray]{
Vivamus et sem velit.
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aliquam erat volutpat.
Sed rhoncus neque a orci vulputate ut elementum dui ornare.
}
\highlight[yellow]{
Nulla id magna metus. Integer lacus dolor, tempus ac sodales
eu, blandit nec ligula.
Etiam quis arcu ac nisi lobortis ultricies quis in dolor.
Quisque lobortis magna arcu.
}
\end{document}